This lesson includes 10 additional questions and 123 additional question variations for subscribers.

# Lesson Worksheet: Areas and Circumferences of Circles Mathematics

In this worksheet, we will practice finding the area and the circumference of a circle given its radius or diameter and relating both the area and circumference to solve various problems.

**Q2: **

With circles and touching at
, the shaded area is 331 cm^{2}. Given that
, determine the sum
of the two radii correct to the nearest hundredth.

**Q3: **

Emma is interested in finding the formula for the area of a circle. She has studied how to find the circumference of a circle and knows the formula . She has seen a picture of a series of concentric circles and wants to use that to work out the area of a circle. She has a series of circular rings made of string and organizes them as seen in the given picture. She then cuts them at a single point and places them, keeping the distances between the rings the same as they were in the circle, to form the triangle shown.

What can be said about the radius of the orginal circle and the height of the triangle?

- AThe height is half the radius.
- BThe radius is longer than the height.
- CThey are equal.
- DThe radius is shorter than the height.
- EThe height is twice the radius.

The base of the triangle must be equal to the circumference of the circle. If the circle has radius , what is the length of the base of the triangle?

- A
- B
- C
- D
- E

In terms of and , work out the area of the triangle. Fully simplify your result.

- A
- B
- C
- D
- E

After this experiment, what formula do you think Emma decided to use to work out the area of a circle?

- A
- B
- C
- D
- E

**Q4: **

Given that the area of a circle is 49,896 cm^{2},
find its radius. (Taking ).

**Q6: **

Using 3.14 as an approximation to , calculate the area of the shaded region.

**Q8: **

The bull’s eye on the given archery target has a radius of 3 in. The entire target has a radius of 15 in. Determine the area of the target outside of the bull’s eye rounded to the nearest square inch.

**Q9: **

Using 3.14 in place of , determine the radius of a circle whose area is 153.86.

**Q10: **

A circle has a circumference of 90 cm.

Work out the square of the circumference.

- A8,100
- B180
- C16,200
- D810
- E90

Divide the square of the circumference by , giving your answer accurate to two decimal places.

- A1,289.16
- B14.32
- C644.58
- D64.46
- E7.16

Work out the radius of the circle to three decimal places.

Work out the area of the circle. Round your answer to two decimal places.

- A644.58 cm
^{2} - B481.68 cm
^{2} - C4,050.00 cm
^{2} - D340.65 cm
^{2} - E1,289.16 cm
^{2}