Worksheet: Volume of a Pyramid

In this worksheet, we will practice finding the volumes of pyramids with triangular, quadrilateral, or pentagonal bases.

Q1:

If the base area of the shown solid is 1,970 cm2, determine, to the nearest tenth, its volume.

Q2:

Determine, to the nearest hundredth, the volume of the given pyramid.

Q3:

Find the volume of the following regular pyramid rounded to the nearest hundredth.

Q4:

Find the volume of a pentagonal pyramid with a base area of 594 square feet and a height of 8 feet.

Q5:

Determine, to the nearest tenth, the volume of a square pyramid whose base length is 24 cm and slant height is 39 cm.

Q6:

A square pyramid whose base’s side length is 14 cm has a total surface area of 784 cm2. Find its volume to the nearest hundredth.

Q7:

Find the volume of a right square pyramid whose height is 45 cm and base side length is 25 cm.

  • A 16,875 cm3
  • B 28,125 cm3
  • C 3,125 cm3
  • D 9,375 cm3

Q8:

A triangular pyramid has a triangle with base 9.5 and height 8. If the height of the pyramid is 12.2, what is its volume, to the nearest hundredth?

Q9:

Find the height of a regular pyramid whose volume is 196 cm3 and base area is 42 cm2.

Q10:

Given that a square pyramid has a volume of 372 cm3 and a height of 31 cm, determine the perimeter of its base.

  • A 36 cm
  • B 6 cm
  • C 124 cm
  • D 24 cm

Q11:

Determine, to the nearest tenth, the volume of the given solid.

Q12:

Find the volume of a pyramid that has a height of 9.1 yards and a square base of side 7.1 yards to the nearest hundredth.

Q13:

Work out the volume of a square-based pyramid with a height of 4.5 inches and a base length of 2.3 inches. Give your solution as a fraction in its simplest form.

  • A 6 9 2 0 i n 3
  • B 4 7 6 1 2 0 0 i n 3
  • C 6 2 1 4 0 i n 3
  • D 1 5 8 7 2 0 0 i n 3
  • E 1 8 6 3 4 0 i n 3

Q14:

Determine, to the nearest tenth, the volume of a right square pyramid having a base area of 1,398 cm2 and a slant height of 66 cm.

Q15:

Given that a square pyramid has a base area of 4 cm2, and the length of its lateral edge is 48 cm, determine its volume to the nearest hundredth.

Q16:

A rectangular pyramid has a base 30 inches by 25 inches and a height of 43 inches. Which of the following is the closest to the volume of the pyramid?

  • A 75 ft3
  • B 7 ft3
  • C 112 ft3
  • D 6 ft3
  • E 18.7 ft3

Q17:

A triangular pyramid has a right-triangle-shaped base with a leg of 3 centimeters, a hypotenuse of 5 c e n t i m e t e r s , and a volume of 132 cubic centimeters. Find its height.

Q18:

A 24 cm high pyramid is on rhombus-shaped base with diagonals 15 cm and 11 cm. What is its volume?

Q19:

A shape is made up of two pyramids, each with a perpendicular height of 19 inches. They are connected by their bases which are both 10-by-10-inch squares. Work out the volume of the shape, giving your answer to two decimal places.

Q20:

El Castillo, the pyramid at Chichen Itza in Mexico, is 30 metres tall with a volume of about 3 0 5 8 0 cubic metres. Find the length of a side of the square base rounding the result to one decimal place.

Q21:

A square pyramid has a volume of 4,536 cubic inches. What is the volume of this pyramid in cubic feet?

Q22:

Work out the volume of a square-based pyramid with a height of 12 inches and a base length of 5 inches.

Q23:

𝑀 𝐴 𝐵 𝐶 is a triangular pyramid whose vertex 𝑀 is at a distance of 22 cm from its base 𝐴 𝐵 𝐶 . Given that the side lengths of its triangular base are 3 cm, 5 cm, and 4 cm , determine its volume.

  • A 66 cm3
  • B 88 cm3
  • C 132 cm3
  • D 44 cm3

Q24:

A square pyramid has a base diagonal 2 4 √ 2 cm and lateral surface area 720 cm2. What is its volume?

Q25:

A regular pyramid with a square base has a lateral edge length of 15. Find its volume to the nearest hundredth.

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