# Lesson Worksheet: Volumes of Triangular and Quadrilateral Pyramids Mathematics • 8th Grade

In this worksheet, we will practice finding volumes of triangular or quadrilateral pyramids and solving problems including real-life situations.

**Q3: **

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

**Q5: **

The triangle which forms the base of a triangular pyramid has a base of 9.5, and a height of 8. The height of the pyramid itself is 12.2. What is the volume of the pyramid to the nearest hundredth?

**Q9: **

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.

**Q10: **

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

**Q11: **

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.

**Q12: **

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.

**Q13: **

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?

- A112 ft
^{3} - B7 ft
^{3} - C18.7
ft
^{3} - D75 ft
^{3} - E6 ft
^{3}

**Q14: **

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.

**Q15: **

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

**Q16: **

El Castillo, the pyramid at Chichen Itza in Mexico, is 30 meters tall with a volume of about 30,580 cubic meters. Find the length of a side of the square base rounding the result to one decimal place.

**Q18: **

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.

- A44 cm
^{3} - B132
cm
^{3} - C66 cm
^{3} - D88 cm
^{3}

**Q19: **

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

**Q20: **

is a right pyramid whose base is a square of side length 6 cm, and . Find the pyramid’s volume rounded to the nearest hundredth.

**Q21: **

Given that is a cube of edge length 8 cm, determine, in cubic centimeters, the volume of the pyramid to the nearest hundredth.

**Q22: **

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

**Q23: **

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.

**Q24: **

The Louvre Pyramid in Paris has a square base whose sides are 112 feet long. Given that its volume is 296,875 cubic feet, find the height of the pyramid to the nearest foot.

**Q25: **

Find the volume of the following regular pyramid approximating the result to the nearest hundredth.