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In this lesson, we will learn how to find the volumes of pyramids with triangular, quadrilateral, or pentagonal bases.

Q1:

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

Q2:

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

Q3:

If the base area of the shown solid is 1 970 cm^{2}, determine, to the nearest tenth, its volume.

Q4:

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

Q5:

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

Q6:

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.

Q7:

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

Q8:

Determine, to the nearest tenth, the volume of a square pyramid whose base length is 74 cm and slant height is 64 cm.

Q9:

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

Q10:

A regular pyramid with a square base has a lateral edge length of 23. Find its volume to the nearest hundredth.

Q11:

𝑀 𝐴 𝐵 𝐶 𝐷 is a right pyramid whose base 𝐴 𝐵 𝐶 𝐷 is a square of side length 6 cm, and 𝑀 𝐴 = 𝑀 𝐵 = 𝑀 𝐶 = 𝑀 𝐷 = 4 9 c m . Find the pyramid’s volume rounded to the nearest hundredth.

Q12:

Given that 𝐴 𝐵 𝐶 𝐷 𝐴 ′ 𝐵 ′ 𝐶 ′ 𝐷 ′ is a cube of edge length 8 cm, determine, in cubic centimetres, the volume of the pyramid 𝐵 ′ 𝐴 𝐵 𝐶 to the nearest hundredth.

Q13:

A square pyramid has base with diagonal 2 0 √ 2 cm. If its slant height is 17 cm, what is its volume? Give your answer to the nearest hundredth.

Q14:

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.

Q15:

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

Q16:

A square pyramid whose base’s side length is 14 cm has a total surface area of 784 cm^{2}. Find its volume to the nearest hundredth.

Q17:

A square pyramid has a base measuring 24 by 24 inches and a height of 5 inches. Find the surface area and the volume of the pyramid.

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:

Work out the volume of a square-based pyramid with a base length of 3 feet and a perpendicular height of 86 inches. Give your answer in cubic feet.

Q21:

Given that a square pyramid has a base area of 4 cm^{2}, and the length of its lateral edge is 48 cm, determine its volume to the nearest hundredth.

Q22:

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.

Q23:

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.

Q24:

Determine, to the nearest tenth, the volume of a right square pyramid having a base area of 1 398 cm^{2} and a slant height of 66 cm.

Q25:

The Louvre Pyramid in Paris has a square base whose sides are 112 feet long. Given that its volume is 2 9 6 8 7 5 cubic feet, find the height of the pyramid to the nearest foot.

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