Question

1. A circle has a circumference of 37.54 feet find the radius use 3.14 for pi

2. The circle has a diameter of 20 inches. What is the area in terms for pi.

3. Find the following if the diameter =24cm , the radius, circumference and the area

Answer 1

Explanation:

1. R = 37.54 : 2 : 3.14 = 5.977707.... (round to 6)

2. We find the radius first : 20/2 = 10 inches
A = 10.10.3.14 = 314 = 100pi

3.
Radius = 24 : 2 = 12cm
Circumference = approx. 75.4cm
Area = 452.16cm2

Answer 2

1. r = 5.98 ft (2 dp)

2. area = 100
`\pi` in²

3. radius = 12 cm

circumference = 24
`\pi` cm ≈ 75.398 cm (3 dp)

area = 144
`\pi` cm² ≈ 452.389 cm² (3 dp)

Explanation:

1. circumference of a circle =
`2\pi r` (where r is the radius)

Given:

• circumference = 37.54 ft
• 
  `\pi` = 3.14

⇒ 37.54 = 2 x 3.14 x r

⇒ 37.54 = 6.28 r

⇒ r = 37.54 ÷ 6.28

⇒ r = 5.98 ft (2 dp)

2. area of a circle =
`\pi r^2` (where r is the radius)

radius =
`\frac12d` (where d is the diameter)

Given:

• diameter = 20 in

⇒ area =
`\pi` x 10²

⇒ area = 100
`\pi` in²

3. radius =
`\frac12d` (where d is the diameter)

circumference of a circle =
`2\pi r` (where r is the radius)

area of a circle =
`\pi r^2` (where r is the radius)

Given:

• diameter = 24 cm

⇒ radius = 1/2 x 24 = 12 cm

⇒ circumference = 2 x
`\pi` x 12 = 24
`\pi` cm

⇒ area =
`\pi` x 12² = 144
`\pi` cm²