﻿ Circles Worksheet | Problems & Solutions

# Circles Worksheet

Circles Worksheet
• Page 1
1.
Choose the correct statement(s).
(i) diameter of a circle = 2 × radius
(ii) diameter of a circle = $\frac{1}{2}$× radius
(iii) radius of a circle = 2 × diameter
(iv) radius of a circle = $\frac{1}{2}$× diameter
 a. (iii) and (iv) only b. (i) and (ii) only c. (i) and (iv) only d. (ii) and (iii) only

#### Solution:

The diameter of a circle is the line segment which passes through the center and whose end points lie on the circle.

The distance from the center of a circle to any point on the circle is called the radius.

Therefore from the definitions of diameter and radius, we can say that diameter is twice the radius. This also implies that radius is half of the diameter.

From the given choices, (i) and (iv) only is the correct answer.

2.
Find the diameter of the circle whose radius is 5 cm.
 a. 9 cm b. 12 cm c. 10 cm d. 11 cm

#### Solution:

= 2 × 5 cm.

= 10 cm
[Multiply]

So, the diameter of the circle is 10 cm.

3.
Which of the given statements is true?
 a. diameter = $\frac{2}{radius}$ b. diameter = 2 - radius c. diameter = $\frac{1}{2}$ × radius d. diameter = 2 × radius

#### Solution:

The length of the diameter of a circle is two times the radius of the circle.

4.
Find the radius of the circle whose diameter is 22 cm.
 a. 44 cm b. 10 cm c. 11 cm d. 22 cm

#### Solution:

[Divide each side by 2.]

[Substitute diameter = 22.]

[Divide.]

5.
How many circles are there?

 a. 1 b. 3 c. 5 d. 2

#### Solution:

A circle is a plane figure made up of points that are all at the same distance from the center point.

Among the figures, (c) and (e) are circles.

There are 2 circles in the figures.

6.
O is the center of the circle. Which line segment is not the radius of the circle?

 a. OD b. AB c. OE d. OA

#### Solution:

A line segment joining the center and any point on the circle is called the radius of the circle.

A and B are two points on the circle. So, line joining A and B cannot be the radius of the circle.

7.
Find the diameter of a circle, if its radius is 3 cm.
 a. 1.5 cm b. 5 cm c. 9 cm d. 6 cm

#### Solution:

[Formula.]

= 2 × 3

= 6
[Multiply.]

The diameter of the circle is 6 cm.

8.
If O is the center of the circle, then find the radius of the circle.

 a. 5 cm b. 20 cm c. 10 cm d. 15 cm

#### Solution:

A diameter is a line segment, whose end points always lie on the circle and that passes through the center of the circle.

[Formula.]

[Divide each side by 2.]

[Substitute 10 for diameter.]

[Divide.]

The radius of the circle is 5 cm.

9.
The diameter of a circular bed is 12 feet. What is its radius?
 a. 6 feet b. 5 feet c. 24 feet d. 10 feet

#### Solution:

[Formula.]

[Divide each side by 2.]

[Substitute 12 for diameter.]

[Divide.]

So, the radius of the circular bed is 6 feet.

10.
A circular swimming pool is constructed with a radius of 14 feet. What is its diameter?
 a. 27 feet b. 29 feet c. 14 feet d. 28 feet

[Formula.]

= 2 × 14