Area, Surface Area, and Volume: math test, Grade 10 – download the PDF

1 A shed wall / 3 pts

The front wall of a shed is a 10 m by 6 m rectangle topped by a triangle of height 4 m (the triangle’s base is the 10 m side).

1. Find the area of the wall.
2. Paint costs 3.50 dollars per square meter. How much does it cost to paint the wall?

2 A fish tank / 3 pts

An open-top fish tank is a rectangular prism 60 cm long, 30 cm wide, and 40 cm high. (1 L = 1,000 cm³.)

1. Find its capacity in liters.
2. How much water is in it when it is three-quarters full?
3. Find the area of glass needed (no top).

3 Cylinder and cone / 4 pts

A cylinder and a cone both have radius 4 cm and height 9 cm. Give exact values and decimals to the nearest hundredth.

1. Volume of the cylinder.
2. Volume of the cone.
3. Total surface area of the cylinder.
4. How many times does the cone fit in the cylinder?

4 A ball / 3 pts

A ball has diameter 24 cm.

1. Find its surface area and its volume in terms of \(\pi\).
2. How many liters of air does it hold, to the nearest hundredth? (1 L = 1,000 cm³.)

5 Slicing a pyramid / 4 pts

A square pyramid has base side 16 cm and height 12 cm. A plane parallel to the base is 3 cm above the base.

1. Find the volume of the pyramid.
2. Find the side and the area of the cross section.
3. Find the volume of the small pyramid above the plane.

6 Steel ball and Cavalieri / 3 pts

A solid steel ball has radius 3 cm and density 7.85 g/cm³.

1. Find its volume to the nearest hundredth.
2. Find its mass to the nearest tenth of a gram.
3. A stack of 50 identical cards is straight; another is leaning, with the same height. Explain why both have the same volume.