Circles, Area, Surface Area and Volume: math practice, Grade 7 – download the PDF

1 Radius or diameter? ★★★

Complete each statement.

1. A circle has a diameter of 14 cm, so its radius is ___.
2. A circle has a radius of 2.5 in, so its diameter is ___.
3. A circle has a diameter of 9 ft, so its radius is ___.

2 Fencing a pond ★★★

A circular pond has a diameter of 12 m. A fence will go all the way around it. How long is the fence? Use \(\pi \approx 3.14\).

3 A small circle ★★★

Find the area of a circle with a radius of 5 cm. Use \(\pi \approx 3.14\).

4 Triangle and parallelogram ★★★

1. A triangle has a base of 14 in and a height of 9 in. Find its area.
2. A parallelogram has a base of 11 cm and a height of 6 cm. Find its area.

5 True or false? ★★★

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

1. If you double the radius of a circle, its area is doubled. (Test with \(r = 3\) and \(r = 6\), using \(\pi \approx 3.14\).)
2. The circumference of a circle is a little more than three times its diameter.
3. The diameter of a circle is half of its radius.

6 Aquarium volume ★★★

A rectangular aquarium is 24 in long, 10 in wide and 12 in tall. What is its volume?

7 Wrapping a cube ★★★

A gift box is a cube with edges of 5 cm. How much wrapping paper is needed to cover it exactly, with no overlap?

8 Trapezoid garden bed ★★★

A garden bed is a trapezoid. Its parallel sides measure 7 m and 13 m, and the distance between them is 5 m. Find its area.

9 Bicycle wheel ★★★

The wheel of a bicycle has a diameter of 26 in. How far does the bike travel when the wheel makes 50 full turns? Give the answer in inches and in feet, to the nearest tenth. Use \(\pi \approx 3.14\).

10 From circumference to radius ★★★

A circular table has a circumference of 47.1 cm in a scale model. Find its diameter and its radius. Use \(\pi \approx 3.14\).

11 Which pizza deal? ★★★

A pizzeria sells one 12-inch pizza, or two 8-inch pizzas for the same price. (The size is the diameter.) Which choice gives more pizza? By how much? Use \(\pi \approx 3.14\).

12 Garden with a pond ★★★

A rectangular garden is 15 m long and 8 m wide. A circular pond of radius 2 m is in the middle of it. How much of the garden is not covered by the pond? Use \(\pi \approx 3.14\).

13 Tent fabric ★★★

A tent is a right triangular prism lying on one of its rectangular faces. Each triangular end has a base of 6 ft and a height of 4 ft, and its two slanted sides measure 5 ft each. The tent is 9 ft long. The floor is also made of fabric. How many square feet of fabric are needed in all?

14 Volume of a ramp ★★★

A wooden ramp is a right prism whose base is a triangle with a base of 10 cm and a height of 6 cm. The prism is 15 cm tall. Find its volume.

15 A pyramid-shaped box ★★★

A square pyramid has a base side of 10 cm and a slant height of 13 cm. Find its surface area.

16 Find the missing measurement ★★★

1. A parallelogram has an area of 84 cm² and a base of 12 cm. Find its height.
2. A triangle has an area of 45 in² and a height of 9 in. Find its base.

17 The sports field ★★★

A sports field is a rectangle 80 m long and 50 m wide with a semicircle added at each short end (the diameter of each semicircle is the 50 m side). Use \(\pi \approx 3.14\).

1. Find the distance around the field.
2. Find the area of the field.
3. A runner jogs 3 times around the field. How far does the runner go?

18 Path around a fountain ★★★

A round fountain has a radius of 4 m. A circular stone path 1.5 m wide goes all the way around it. Find the area of the path to the nearest tenth of a square meter. Use \(\pi \approx 3.14\).

19 Filling a water tank ★★★

A rectangular water tank is 2 m long, 1.5 m wide and 1.2 m tall. A pump fills it at 45 liters per minute, starting from empty. (Recall \(1 \text{ m}^3 = 1{,}000\) L.)

1. Find the volume of the tank in cubic meters.
2. How many liters does it hold?
3. How many minutes does the pump need to fill it?

20 A box without a lid ★★★

A cardboard storage box is a rectangular prism 30 cm long, 20 cm wide and 15 cm tall. It has a bottom but no lid. How much cardboard is used? Show every face you count.

21 Swimming pool ★★★

The cross section of a pool is the trapezoid below. The pool is 20 m wide, 1 m deep at the shallow end and 3 m deep at the deep end. The pool is 10 m long, so it is a right prism whose bases are the trapezoids.

1. Find the area of the trapezoid.
2. Find the volume of the pool.
3. How many liters of water does it hold when full? (\(1 \text{ m}^3 = 1{,}000\) L)

22 Find the error ★★★

A student must find the area of a circle with a diameter of 10 cm. The student writes: \(A = 3.14 \times 10^2 = 314\) cm².

1. Explain the mistake.
2. Give the correct area.
3. By what factor was the student’s answer too large?