# 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.

Q1:

Determine, to the nearest hundredth, the volume of the given pyramid. Q2:

Find the volume of the following regular pyramid rounded to the nearest hundredth. Q3:

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

Q4:

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

Q6:

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

Q7:

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

• A24 cm
• B36 cm
• C124 cm
• D6 cm

Q8:

Determine, to the nearest tenth, the volume of the given solid. 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 cm2 and a slant height of 66 cm.

Q12:

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.

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 ft3
• B7 ft3
• C18.7 ft3
• D75 ft3
• E6 ft3

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.

Q17:

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

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 cm3
• B132 cm3
• C66 cm3
• D88 cm3

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. 