Measurement and Geometry — Civil Service Exam Practice Questions

200 free civil service exam reviewer questions on Measurement and Geometry (Numerical Ability), each with the correct answer and a worked solution.

  1. The diagonal of a square is 4 cm. What is its area?
  2. The length and width of a rectangle are in the ratio 4 : 3, and its perimeter is 70 m. What is its area?
  3. A rectangular tank 1 m × 1 m × 1 m is filled by a hose delivering 40 liters per minute. How long will it take to fill the tank?
  4. A 10-m ladder leans against a wall with its foot 6 m from the wall. How high up the wall does it reach?
  5. How many diagonals does a polygon with 7 sides have?
  6. A garden 34 m by 30 m is surrounded by a walkway 1 m wide. What is the area of the walkway?
  7. A circle is inscribed in a square with sides of 12 cm. What is the area of the region inside the square but outside the circle? (π = 3.14)
  8. What is the volume of a sphere with a radius of 15 cm? (π = 3.14)
  9. What is the volume of a cone with a radius of 6 cm and a height of 14 cm? (π = 3.14)
  10. A cylindrical water tank has a radius of 80 cm and a height of 90 cm. How many liters can it hold? (π = 3.14, 1 L = 1000 cm³)
  11. A window is shaped like a 15 dm × 15 dm rectangle topped by a semicircle whose diameter is the 15-dm side. What is the window's total…
  12. A runner moves at 17 m/s. How far in kilometers does she travel in 17 minutes?
  13. An open-top box (no lid) is 14 cm long, 26 cm wide and 10 cm high. What is the area of material used?
  14. A solid metal cube with 15-cm edges is dropped into a rectangular aquarium 48 cm long and 32 cm wide, fully submerging it. By how much…
  15. A right triangle has a hypotenuse of 15 cm and one leg of 9 cm. What is its area?
  16. A rhombus has diagonals of 10 cm and 27 cm. What is its area?
  17. On a map with scale 1 cm : 500 m, a park occupies 12 cm². What is its actual area?
  18. A lot measures 10,000 m². If land sells for ₱11,500 per square meter, how much does the lot cost, and how many hectares is it?
  19. Each exterior angle of a regular polygon measures 60°. How many sides does it have?
  20. A rice field of 15 hectares yields an average of 139 cavans per hectare. If palay sells for ₱1,200 per cavan, what is the total value of…
  21. A circle has an area of 452.16 m². What is its circumference? (π = 3.14)
  22. A rectangular tank 3 m × 2 m × 1 m is filled by a hose delivering 40 liters per minute. How long will it take to fill the tank?
  23. A 1-m pole casts a shadow 4 m long. At the same time, a building casts a shadow 48 m long. How tall is the building?
  24. If the edge is multiplied by 3, by what factor does the volume of a cube increase?
  25. How many diagonals does a polygon with 8 sides have?
  26. A garden 12 m by 11 m is surrounded by a walkway 2 m wide. What is the area of the walkway?
  27. A circle is inscribed in a square with sides of 38 cm. What is the area of the region inside the square but outside the circle? (π = 3.14)
  28. What is the volume of a cone with a radius of 12 cm and a height of 8 cm? (π = 3.14)
  29. A cylindrical water tank has a radius of 40 cm and a height of 180 cm. How many liters can it hold? (π = 3.14, 1 L = 1000 cm³)
  30. A window is shaped like a 12 dm × 4 dm rectangle topped by a semicircle whose diameter is the 4-dm side. What is the window's total area?…
  31. A runner moves at 23 m/s. How far in kilometers does she travel in 11 minutes?
  32. An open-top box (no lid) is 23 cm long, 18 cm wide and 6 cm high. What is the area of material used?
  33. A solid metal cube with 10-cm edges is dropped into a rectangular aquarium 44 cm long and 51 cm wide, fully submerging it. By how much…
  34. A rhombus has diagonals of 30 cm and 5 cm. What is its area?
  35. On a map with scale 1 cm : 250 m, a park occupies 7 cm². What is its actual area?
  36. A lot measures 10,650 m². If land sells for ₱2,000 per square meter, how much does the lot cost, and how many hectares is it?
  37. A rice field of 3 hectares yields an average of 135 cavans per hectare. If palay sells for ₱1,200 per cavan, what is the total value of…
  38. The diagonal of a square is 20 cm. What is its area?
  39. The length and width of a rectangle are in the ratio 3 : 2, and its perimeter is 60 m. What is its area?
  40. The four walls of a room 4 m by 3 m with a 2.5-m ceiling are to be painted. There is a door of 2 m² and windows totaling 1 m². If 1 liter…
  41. A rectangular tank 3 m × 1 m × 2 m is filled by a hose delivering 20 liters per minute. How long will it take to fill the tank?
  42. A 50-m ladder leans against a wall with its foot 14 m from the wall. How high up the wall does it reach?
  43. If the radius is multiplied by 3, by what factor does the volume of a sphere increase?
  44. How many diagonals does a polygon with 16 sides have?
  45. A garden 21 m by 10 m is surrounded by a walkway 2 m wide. What is the area of the walkway?
  46. What is the volume of a sphere with a radius of 12 cm? (π = 3.14)
  47. What is the volume of a cone with a radius of 6 cm and a height of 9 cm? (π = 3.14)
  48. A cylindrical water tank has a radius of 70 cm and a height of 180 cm. How many liters can it hold? (π = 3.14, 1 L = 1000 cm³)
  49. A window is shaped like a 15 dm × 9 dm rectangle topped by a semicircle whose diameter is the 9-dm side. What is the window's total area?…
  50. A runner moves at 28 m/s. How far in kilometers does she travel in 10 minutes?
  51. An open-top box (no lid) is 25 cm long, 25 cm wide and 12 cm high. What is the area of material used?
  52. A solid metal cube with 20-cm edges is dropped into a rectangular aquarium 59 cm long and 25 cm wide, fully submerging it. By how much…
  53. A right triangle has a hypotenuse of 26 cm and one leg of 10 cm. What is its area?
  54. A rhombus has diagonals of 10 cm and 10 cm. What is its area?
  55. On a map with scale 1 cm : 200 m, a park occupies 8 cm². What is its actual area?
  56. A lot measures 18,350 m². If land sells for ₱13,500 per square meter, how much does the lot cost, and how many hectares is it?
  57. A rice field of 2.5 hectares yields an average of 85 cavans per hectare. If palay sells for ₱1,200 per cavan, what is the total value of…
  58. A circle has an area of 78.5 m². What is its circumference? (π = 3.14)
  59. The diagonal of a square is 28 cm. What is its area?
  60. The length and width of a rectangle are in the ratio 5 : 2, and its perimeter is 84 m. What is its area?
  61. The four walls of a room 3 m by 6 m with a 2.5-m ceiling are to be painted. There is a door of 2 m² and windows totaling 2 m². If 1 liter…
  62. A rectangular tank 1 m × 1 m × 2 m is filled by a hose delivering 40 liters per minute. How long will it take to fill the tank?
  63. A 3-m pole casts a shadow 6 m long. At the same time, a building casts a shadow 66 m long. How tall is the building?
  64. A garden 20 m by 6 m is surrounded by a walkway 2 m wide. What is the area of the walkway?
  65. A circle is inscribed in a square with sides of 8 cm. What is the area of the region inside the square but outside the circle? (π = 3.14)
  66. What is the volume of a cone with a radius of 3 cm and a height of 10 cm? (π = 3.14)
  67. A cylindrical water tank has a radius of 90 cm and a height of 90 cm. How many liters can it hold? (π = 3.14, 1 L = 1000 cm³)
  68. A window is shaped like a 9 dm × 13 dm rectangle topped by a semicircle whose diameter is the 13-dm side. What is the window's total area?…
  69. A runner moves at 28 m/s. How far in kilometers does she travel in 26 minutes?
  70. An open-top box (no lid) is 23 cm long, 22 cm wide and 13 cm high. What is the area of material used?
  71. A solid metal cube with 10-cm edges is dropped into a rectangular aquarium 50 cm long and 54 cm wide, fully submerging it. By how much…
  72. A right triangle has a hypotenuse of 51 cm and one leg of 24 cm. What is its area?
  73. A rhombus has diagonals of 10 cm and 25 cm. What is its area?
  74. On a map with scale 1 cm : 250 m, a park occupies 3 cm². What is its actual area?
  75. A lot measures 10,200 m². If land sells for ₱7,000 per square meter, how much does the lot cost, and how many hectares is it?
  76. Each exterior angle of a regular polygon measures 40°. How many sides does it have?
  77. A rice field of 6.5 hectares yields an average of 130 cavans per hectare. If palay sells for ₱1,000 per cavan, what is the total value of…
  78. A circle has an area of 379.94 m². What is its circumference? (π = 3.14)
  79. The diagonal of a square is 10 cm. What is its area?
  80. The four walls of a room 3 m by 4 m with a 2.5-m ceiling are to be painted. There is a door of 2 m² and windows totaling 4 m². If 1 liter…
  81. A rectangular tank 4 m × 2 m × 1 m is filled by a hose delivering 40 liters per minute. How long will it take to fill the tank?
  82. A 51-m ladder leans against a wall with its foot 24 m from the wall. How high up the wall does it reach?
  83. If the radius is multiplied by 4, by what factor does the area of a circle increase?
  84. How many diagonals does a polygon with 19 sides have?
  85. A garden 40 m by 36 m is surrounded by a walkway 3 m wide. What is the area of the walkway?
  86. A circle is inscribed in a square with sides of 16 cm. What is the area of the region inside the square but outside the circle? (π = 3.14)
  87. What is the volume of a cone with a radius of 6 cm and a height of 10 cm? (π = 3.14)
  88. A cylindrical water tank has a radius of 80 cm and a height of 160 cm. How many liters can it hold? (π = 3.14, 1 L = 1000 cm³)
  89. A window is shaped like a 15 dm × 16 dm rectangle topped by a semicircle whose diameter is the 16-dm side. What is the window's total…
  90. A runner moves at 17 m/s. How far in kilometers does she travel in 13 minutes?
  91. An open-top box (no lid) is 12 cm long, 20 cm wide and 19 cm high. What is the area of material used?
  92. A solid metal cube with 20-cm edges is dropped into a rectangular aquarium 38 cm long and 33 cm wide, fully submerging it. By how much…
  93. A right triangle has a hypotenuse of 5 cm and one leg of 3 cm. What is its area?
  94. A rhombus has diagonals of 18 cm and 13 cm. What is its area?
  95. A lot measures 15,050 m². If land sells for ₱3,500 per square meter, how much does the lot cost, and how many hectares is it?
  96. Each exterior angle of a regular polygon measures 30°. How many sides does it have?
  97. A rice field of 12 hectares yields an average of 110 cavans per hectare. If palay sells for ₱1,200 per cavan, what is the total value of…
  98. A circle has an area of 706.5 m². What is its circumference? (π = 3.14)
  99. The diagonal of a square is 8 cm. What is its area?
  100. The length and width of a rectangle are in the ratio 8 : 5, and its perimeter is 156 m. What is its area?
  101. A rectangular tank 1 m × 3 m × 2 m is filled by a hose delivering 100 liters per minute. How long will it take to fill the tank?
  102. A 15-m ladder leans against a wall with its foot 9 m from the wall. How high up the wall does it reach?
  103. A 2-m pole casts a shadow 6 m long. At the same time, a building casts a shadow 42 m long. How tall is the building?
  104. If the radius is multiplied by 4, by what factor does the volume of a sphere increase?
  105. How many diagonals does a polygon with 22 sides have?
  106. A garden 15 m by 11 m is surrounded by a walkway 1 m wide. What is the area of the walkway?
  107. A circle is inscribed in a square with sides of 6 cm. What is the area of the region inside the square but outside the circle? (π = 3.14)
  108. What is the volume of a sphere with a radius of 9 cm? (π = 3.14)
  109. What is the volume of a cone with a radius of 3 cm and a height of 3 cm? (π = 3.14)
  110. A cylindrical water tank has a radius of 10 cm and a height of 60 cm. How many liters can it hold? (π = 3.14, 1 L = 1000 cm³)
  111. Convert -5 °C to degrees Fahrenheit.
  112. Convert 72 km/h to meters per second.
  113. Convert 42 inches to cm. (1 inch = 2.54 cm)
  114. The legs of a right triangle measure 21 cm and 72 cm. How long is the hypotenuse?
  115. What is the total surface area of a cube with edges of 11 cm?
  116. What is the volume of a box 19 cm long, 3 cm wide and 2 cm high?
  117. A trapezoid has parallel sides of 30 m and 40 m and a height of 16 m. What is its area?
  118. What is the area of a circle with a radius of 5 m? (Use π = 3.14)
  119. A rectangular lot 40 m by 19 m is to be fenced at ₱170 per meter. How much will the fence cost?
  120. How many 40 cm × 40 cm square tiles are needed to cover a floor 10.8 m by 2.4 m?
  121. Convert 41 °F to degrees Celsius.
  122. Convert 38 miles to km. (1 mil = 1.609 km)
  123. The legs of a right triangle measure 24 cm and 45 cm. How long is the hypotenuse?
  124. What is the volume of a box 17 cm long, 12 cm wide and 7 cm high?
  125. A trapezoid has parallel sides of 28 m and 44 m and a height of 16 m. What is its area?
  126. What is the area of a circle with a radius of 26 m? (Use π = 3.14)
  127. A rectangular lot 48 m by 20 m is to be fenced at ₱280 per meter. How much will the fence cost?
  128. How many 30 cm × 30 cm square tiles are needed to cover a floor 5.4 m by 0.9 m?
  129. What is the measure of each interior angle of a regular polygon with 9 sides?
  130. What is the sum of the interior angles of a polygon with 12 sides?
  131. Convert -20 °C to degrees Fahrenheit.
  132. Convert 18 km/h to meters per second.
  133. Convert 33 miles to km. (1 mil = 1.609 km)
  134. The legs of a right triangle measure 10 cm and 24 cm. How long is the hypotenuse?
  135. What is the total surface area of a cube with edges of 10 cm?
  136. What is the volume of a box 13 cm long, 11 cm wide and 11 cm high?
  137. A trapezoid has parallel sides of 28 m and 43 m and a height of 12 m. What is its area?
  138. What is the area of a circle with a radius of 16 m? (Use π = 3.14)
  139. A rectangular lot 10 m by 7 m is to be fenced at ₱130 per meter. How much will the fence cost?
  140. How many 20 cm × 20 cm square tiles are needed to cover a floor 1.6 m by 1.2 m?
  141. What is the measure of each interior angle of a regular polygon with 5 sides?
  142. What is the sum of the interior angles of a polygon with 17 sides?
  143. Convert 50 °C to degrees Fahrenheit.
  144. Convert 108 km/h to meters per second.
  145. Convert 13 hectares to m². (1 hectar = 10,000 m²)
  146. The legs of a right triangle measure 16 cm and 30 cm. How long is the hypotenuse?
  147. What is the volume of a box 12 cm long, 3 cm wide and 2 cm high?
  148. A trapezoid has parallel sides of 30 m and 48 m and a height of 22 m. What is its area?
  149. What is the area of a circle with a radius of 27 m? (Use π = 3.14)
  150. A rectangular lot 47 m by 14 m is to be fenced at ₱180 per meter. How much will the fence cost?
  151. What is the measure of each interior angle of a regular polygon with 18 sides?
  152. What is the sum of the interior angles of a polygon with 14 sides?
  153. Convert 212 °F to degrees Celsius.
  154. Convert 126 km/h to meters per second.
  155. Convert 23 inches to cm. (1 inch = 2.54 cm)
  156. The legs of a right triangle measure 6 cm and 8 cm. How long is the hypotenuse?
  157. What is the volume of a cube with edges of 2 cm?
  158. What is the volume of a box 15 cm long, 15 cm wide and 8 cm high?
  159. A trapezoid has parallel sides of 17 m and 49 m and a height of 26 m. What is its area?
  160. What is the area of a circle with a radius of 29 m? (Use π = 3.14)
  161. What is the supplementary of a 26° angle?
  162. What is the area of a triangle with a base of 15 cm and a height of 14 cm?
  163. What is the area of a rectangle measuring 32 m by 9 m?
  164. What is the perimeter of a rectangle 26 m long and 7 m wide?
  165. How many mL are in 60 L?
  166. Two angles of a triangle measure 50° and 89°. What is the third angle?
  167. What is the circumference of a circle with a diameter of 10 cm? (Use π = 3.14)
  168. What is the complementary of a 41° angle?
  169. What is the area of a triangle with a base of 7 cm and a height of 6 cm?
  170. What is the area of a rectangle measuring 30 m by 27 m?
  171. What is the perimeter of a rectangle 30 m long and 8 m wide?
  172. How many cm are in 7.7 m?
  173. Two angles of a triangle measure 77° and 53°. What is the third angle?
  174. What is the circumference of a circle with a diameter of 24 cm? (Use π = 3.14)
  175. What is the complementary of a 81° angle?
  176. What is the area of a triangle with a base of 17 cm and a height of 30 cm?
  177. What is the area of a rectangle measuring 49 m by 45 m?
  178. What is the perimeter of a rectangle 16 m long and 8 m wide?
  179. How many g are in 28 kg?
  180. Two angles of a triangle measure 55° and 58°. What is the third angle?
  181. What is the circumference of a circle with a diameter of 38 cm? (Use π = 3.14)
  182. What is the supplementary of a 39° angle?
  183. What is the area of a triangle with a base of 38 cm and a height of 28 cm?
  184. What is the area of a rectangle measuring 39 m by 34 m?
  185. What is the perimeter of a rectangle 27 m long and 6 m wide?
  186. How many mm are in 8.4 m?
  187. Two angles of a triangle measure 44° and 53°. What is the third angle?
  188. What is the circumference of a circle with a diameter of 29 cm? (Use π = 3.14)
  189. What is the supplementary of a 24° angle?
  190. What is the area of a triangle with a base of 6 cm and a height of 16 cm?
  191. What is the area of a rectangle measuring 42 m by 25 m?
  192. What is the perimeter of a rectangle 5 m long and 4 m wide?
  193. How many mm are in 1.5 m?
  194. Two angles of a triangle measure 74° and 71°. What is the third angle?
  195. What is the circumference of a circle with a diameter of 13 cm? (Use π = 3.14)
  196. What is the supplementary of a 32° angle?
  197. What is the area of a triangle with a base of 20 cm and a height of 26 cm?
  198. What is the area of a square measuring 7 m by 7 m?
  199. What is the perimeter of a rectangle 18 m long and 6 m wide?
  200. How many m are in 8.2 km?