CC Geometry Name______Volume: Prisms and Cylinders Date______Block______

Prism: A solid 3-D object with two identical, parallel bases and flat sides. Prisms are named by their base shape.

The volume formula for any prism:

______

Find the volume of each prism.

1) 2) 3)

4) The cube and the rectangular prism below have the same volume. Find the height of the rectangular prism to the nearest tenth.

Cylinder: A 3-D object that has circles as the bases.

Volume of a cylinder:

Find the volume for each cylinder to the nearest tenth.

1) 2) 3)

Find the volume of each cylinder in terms of 흅.

4) 5)

Word Problems

1) A cylinder has a volume of 1402.4 cm3. If the radius of the base is 6cm, find the height to the nearest tenth.

2) The circumference of the base of a cylinder is 20.1 inches. If the volume of the cylinder is 305.6 in3, find the radius to the nearest tenth.

3) A solid wooden prism has a rectangular base with sides 5 inches, 7 inches and a height of 5 inches. A hole, in the shape of a cylinder with a radius of 1 inch, is drilled through the entire length of the prism. Find the volume remaining in the prism to the nearest cubic inch.

5in

5in 7in

4) A barrel of fuel oil is a right circular cylinder where the inside measurements of the barrel are a diameter of 22.5 inches and a height of 33.5 inches. There are 231 cubic inches in a liquid gallon. Determine and state, to the nearest tenth, the gallons of fuel that are in a barrel of fuel oil.

5) Ian needs to replace two concrete sections in his sidewalk, as modeled below. Each section is 36 inches by 36 inches and 4 inches deep. He can mix his own concrete for $3.25 per cubic foot. How much money will it cost Ian to replace the two concrete sections?

6) A fabricator is hired to make a 27-foot-long solid metal railing for the stairs at the local library. The railing is modeled by the diagram below. The railing is 2.5 inches high and 2.5 inches wide and is comprised of a rectangular prism and a half-cylinder. How much metal, to the nearest cubic inch, will the railing contain?

CC Geometry Name______Practice: Prisms and Pyramids Date______Block______

1) Find the volume of the triangular prism.

2) A gallon of paint will cover approximately 400 square feet. An artist wants to paint all the outside surfaces of a cube measuring 15 feet on each edge. How many gallons of paint will the artist need to buy?

3) The objects below have the same volume. Find the radius of the cylinder to the nearest tenth.

4) A right circular cylinder has a diameter of 5 inches and a height of 15 inches. Find the volume in terms of 휋.

5) The volume of a cylinder is 31810 cm2. If the height is 45cm, find the radius to the nearest integer.

6) A 90° wedge is removed from the right circular cylinder with a radius of 9 inches and a height of 2ft. Find the volume of the remaining portion of the cylinder to the nearest tenth of a cubic inch.

7) A cylinder is to be cut from the square prism below. What is the volume of the remaining solid to the nearest tenth?

8) In the figures below, the volume of the cylinder is DOUBLE that of the cube. Calculate the height of the cylinder to the nearest tenth.

CC Geometry Name______HW – Volume of Prisms and Cylinders Date______Block______

Find the volume of each object.

1) 2) in terms of 휋

3)

4) The two cylinders below have the same volume. Calculate the radius of the taller cylinder to the nearest tenth.

5) A rectangular prism is to be cut out of a cylinder as shown below. What is the volume of the cylinder after the prism is cut out? Round to the nearest tenth of a cubic cm.

6) A gas station has a cylindrical fueling tank that holds the gasoline for its pumps, as modeled below. The tank holds a maximum of 20,000 gallons of gasoline and has a length of 34.5 feet.

A metal pole is used to measure how much gas is in the tank. To the nearest tenth of a foot, how long does the pole need to be in order to reach the bottom of the tank and still extend one foot outside the tank? Justify your answer.