Grade 8 Unit 5 End-of-Unit Assessment

A cylinder has volume 78 cm³. What is the volume of a cone with the same radius and height?

• 26 cm³

• 39 cm³

• 156 cm³

• 234 cm³

The graph shows the relationship between the radius and volume for many cones whose height is 6 inches. Select all the true statements about such cones.

• The relationship between radius and volume is linear.

• The relationship between radius and volume is not linear.

• If the radius of the cone doubles, the volume of the cone doubles.

• If the radius of the cone doubles, the volume of the cone is multiplied by 4.

• If the radius of the cone is 2 inches, the volume of the cone is about 25 cubic inches.

A sphere has radius 2.7 centimeters. What is its volume, to the nearest cubic centimeter?

• 23

• 26

• 62

• 82

For cones with radius 6 units, the equation V = 12πh relates the height h of the cone, in units, and the volume V of the cone, in cubic units. What is the shape of the graph of this equation?

• A straight line

• A parabola

• A circle

• A hyperbola

A cylinder has radius 1.6 meters. Its volume is 95 cubic meters. Find its height to the nearest tenth of a meter.

Problem 6: Cones A and B both have volume 48π cubic units, but have different dimensions. Cone A has radius 6 units and height 4 units. Which of the following is a possible radius and height for Cone B?

• Radius 4 units, Height 9 units

• Radius 3 units, Height 8 units

• Radius 8 units, Height 3 units

• Radius 2 units, Height 12 units

If a cylinder with height 9 inches and radius r is filled with water, it can fill a certain pitcher. How many of these pitchers can a cylinder with height 9 inches and radius 2r fill?

• 2

• 4

• 6

• 8

Which is closest to the difference in the volume of the two cylinders?

• 15,795 cm³

• 2,534 cm³

• 806 cm³

• 512 cm³

A sphere has a volume of 972π cm³. What is its radius in centimeters?

• 4.5

• 9

• 11

• 18

The graph shows the relationship between a sphere’s radius and volume. Select all the statements that are true about this relationship.

• If the radius doubles, the volume doubles.

• If the radius doubles the volume becomes about 4 times bigger.

• If the radius doubles, the volume becomes about 8 times bigger.

• The relationship is linear.

• The relationship is not linear.