# Circle Worksheet

### Solutions

1The wheel of a truck has a radius of 90 cm. How far has the truck travelled when the wheel has rotated 100 times?

2A lighthouse sweeps its light across the horizon with an angle of rotation of 128 degrees. If the maximum range of the beacon is 7 miles, what is the maximum length of the corresponding arc?

3A circle has a circumference of 43.96 cm. What is the area of the circle?

4The area of a circular sector of 90° is 4π cm. Find the radius and length of the circle to which this sector belongs to.

5Calculate the area of a circular sector whose chord is the side of an inscribed equilateral triangle in a circle with a 2 cm radius.

6The surface of a table consists of a square of 1 m per side and two semicircles attached on either opposite end. Calculate the area of the table.

7Calculate the shaded area of the figure below if the radius of the larger circle is 6 cm and the radius of the smaller circles are 2 cm.

8Find the area of the shaded portion of the square ABCD if AB = 10 cm, and APC, AQC are center circle arcs from their centre points B and D respectively.

9Calculate the area of the square inscribed in a circle with a circumference of 18.84 cm.

10A regular hexagon of side 4 cm has a circle inscribed and another circumscribed around its shape. Find the area enclosed between these two concentric circles.

## 1

The wheel of a truck has a radius of 90 cm. How far has the truck travelled when the wheel has rotated 100 times?

r = 90 : 100 = 0.9 m

L = 2 · π · 0.9 = 5.65 m

5.65 · 100 = 565 m

## 2

A lighthouse sweeps its light across the horizon with an angle of rotation of 128 degrees. If the maximum range of the beacon is 7 miles, what is the maximum length of the corresponding arc?

## 3

A circle has a circumference of 43.96 cm. What is the area of the circle?

## 4

The area of a circular sector of 90° is 4π cm. Find the radius and length of the circle to which this sector belongs to.

## 5

Calculate the area of a circular sector whose chord is the side of an inscribed equilateral triangle in a circle with a 2 cm radius.

## 6

The surface of a table consists of a square of 1 m per side and two semicircles attached on either opposite end. Calculate the area of the table.

## 7

Calculate the shaded area of the figure below if the radius of the larger circle is 6 cm and the radius of the smaller circles are 2 cm.

## 8

Find the area of the shaded portion of the square ABCD if AB = 10 cm, and APC, AQC are center circle arcs from their centre points B and D respectively.

The shaded portion consists of two circular segments.

Calculate the area of both circular segments if the circular area of the segment = area of the circular sector − area of triangle.

## 9

Calculate the area of the square inscribed in a circle with a circumference of 18.84 cm.

## 10

A regular hexagon of side 4 cm has a circle inscribed and another circumscribed around its shape. Find the area enclosed between these two concentric circles.