CC Geometry Name______Volume of Pyramids and Cones Date______Block______

The formula for the volume of a pyramid follows directly from the volume of a prism. The pyramid will always be 1/3 the volume of the prism with the same base and height. Pyramids are named by their base shape.

Volume of a pyramid:

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Sometimes with pyramids the height of the solid is not given and we need to calculate it using the Pythagorean Theorem. In this example we have been given the slant height – the height of the triangular face instead of the height of the pyramid.

Example: What is the volume, to the nearest hundredth of a cubic centimeter, of a right square pyramid with base edges that are 26cm long and a slant height of 20cm?

Examples: Find the volume of each pyramid. Round to the nearest tenth if necessary.

1) 2) 3)

4) The volume of a rectangular pyramid is 64in3. If the base dimensions are 4in and 6in, what is the height of the pyramid?

The formula for the volume of a cone follows directly from the volume of a cylinder. The cone will always be 1/3 the volume of the cylinder with the same base radius and height.

Volume of a cone:

Examples: Determine the volume to the nearest tenth.

1) 2) 3)

Determine the volume in terms of 흅.

4) 5) 6)

Mixed problems:

1) Find the volume of the figure in terms of 휋. 2) Find the volume of the figure.

3) A regular pyramid has a square base. The perimeter of the base is 36 inches and the height of the pyramid is 10 inches. What is the volume of the pyramid?

4) A waffle cone can be modeled by a right circular cone with a base diameter of 6cm and a volume of 36 cubic centimeters. What is the number of centimeters in the height of the cone to the nearest tenth?

5) A square pyramid has a height of 8 inches and a volume of 96 in3. What is the length of the side of the base?

CC Geometry Name______Practice – Volume of Pyramids and Cones Date______Block______

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CC Geometry Name______HW – Volume of Pyramids and Cones Date______Block______

Find the volume of each pyramid. Round to the nearest tenth if necessary.

1) 2) 13 23 m

24 12.5 m 24 25 m

Find the volume of each cone in terms of 흅.

3) 4) 18 in.

5 m 15 in.

3 m

5) A sculptor needs to remove a cone shape from a cylindrical block. The diameter of the base of the cylinder is 2 feet and the height is 3 feet. Once the cone is removed, how much volume will be left in the cylinder? Round to the nearest hundredth.

6) A pyramid has a right triangle as its base. The legs are 10 cm and 20 cm, and the volume of the pyramid is 600 cm³. Find the altitude of the pyramid.

7) A water cup in the shape of a cone has a height if 5 inches and a maximum diameter of 3 inches. Find the volume of water in the cup when it is filled to half of its height. Round to the nearest tenth.