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

**Q3: **

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

**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 cm^{2}. Find its volume to the nearest hundredth.

**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?

**Q10: **

Given that a square pyramid has a volume of 372 cm^{3} and a height of 31 cm, determine the perimeter of its base.

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

**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
- B
- C
- D
- E

**Q14: **

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.

**Q15: **

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.

**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 ft
^{3} - B
7 ft
^{3} - C
112 ft
^{3} - D
6 ft
^{3} - E
18.7
ft
^{3}

**Q17: **

A triangular pyramid has a right-triangle-shaped base with a leg of 3 centimeters, a hypotenuse of , 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 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: **

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

- A
66 cm
^{3} - B
88 cm
^{3} - C
132
cm
^{3} - D
44 cm
^{3}

**Q24: **

A square pyramid has a base diagonal cm
and lateral surface area 720 cm^{2}.
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.