Volume of Cylinders, Cones and Spheres: math test, Grade 8 – download the PDF

1 Computing volumes / 4 pts

Give the exact volume in terms of \(\pi\).

1. A cylinder with radius 6 cm and height 5 cm.
2. A cone with radius 6 cm and height 5 cm.
3. A sphere with radius 12 mm.
4. How many of the cones from part b would be needed to fill the cylinder from part a?

2 A big barrel / 3 pts

A barrel is a cylinder with a diameter of 14 in and a height of 9 in. Calculators are allowed. Use \(\pi \approx 3.14\) and \(1 \text{ gallon} = 231 \text{ in}^3\).

1. Find the volume of the barrel to the nearest tenth of a cubic inch.
2. How many gallons does it hold, to the nearest tenth?

3 A missing radius / 3 pts

A cone has a height of 18 cm and a volume of \(150\pi \text{ cm}^3\). Find the radius of its base.

4 A toy / 4 pts

A toy is a cylinder of radius 5 cm and height 12 cm, topped by a hemisphere of radius 5 cm. Calculators are allowed. Use \(\pi \approx 3.14\).

Find the exact volume in terms of \(\pi\), then the volume to the nearest tenth of a cubic centimeter.

5 A ball in a glass / 3 pts

A cylindrical glass has a radius of 4 cm and holds some water. A metal ball of radius 3 cm is dropped in and sinks completely, and no water spills out. By how many centimeters does the water level rise?

6 True or false? / 3 pts

Say whether each statement is true or false, and justify your answer.

1. If you double the height of a cone and keep the same base, its volume doubles.
2. If you double the radius of a cylinder and keep the same height, its volume doubles.
3. The volume of a hemisphere of radius \(r\) is half the volume of a sphere of radius \(r\).