Question

Find the formula for the area A and the perimeter P of the shape shown find the area and perimeter when R is 5 cm find R when A is 100cm2 find r when P is 50cm find the value of r that makes A = p numerically

Answer 1

The formula for the area A and the perimeter P of the shape are Area = 1/4πr² and Perimeter = 1/2πr + 2r

When the radius is 5 cm, the area is 1.99 square cm and the perimeter is 4.80 cm

When the area is 100 square cm, the radius is 11.28 cm

When the perimeter is 50 cm, the radius is 23.16 cm

Finding the formula for the area A and the perimeter P of the shape

From the question, we have the following parameters that can be used in our computation:

The quarter circle

The area of the quarter circle is calculated as

Area = 1/4πr²

The perimeter is the sum of the side lengths

So, we have

Perimeter = 1/2πr + 2r

When r is 5 cm, we have

Area = 1/4π * 5² = 1.99 square cm

Perimeter = 1/2π * 5 + 2 * 2 = 4.80 cm

When A is 100 square cm, the radius (r) is

1/4πr² = 100

r² = 400/π

r² = 127.32

r = 11.28

When P is 50 cm, the radius (r) is

1/2πr + 2r = 50

r(1/2π + 2) = 50

r = 50/(1/2π + 2)

r = 23.16

Hence, the radius is 23.16 cm

Answer 2

1)Area; A = ¼πr²

Perimeter; P = πr/2 + 2r

2)A = 19.63 cm²

P = 17.85 cm

3) r = 8.885 cm

4) r = 14 cm

Explanation:

This is a quadrant of a circle. Thus;

Area of a circle is πr². A quadrant is a quarter of a circle. Thus;

Formula for Quadrant Area is; A = ¼πr²

A) Perimeter of a circle is 2πr. Thus, perimeter of a quadrant is a quarter of the full circle perimeter.

Formula for the quadrant perimeter in the image given is;

P = 2πr/4 + 2r

P = πr/2 + 2r

B) When r is 5 cm;

A = ¼π(5)²

A = 19.63 cm²

P = π(5)/2 + 2(5)

P = 17.85 cm

C) when A is 100cm²:

¼πr² = 100

r² = 100 × 4/π

r² = 78.9358

r = √78.9358

r = 8.885 cm

D) when P = 50 cm.

50 = πr/2 + 2r

50 = (½π + 2)r

r = 50/(½π + 2)

r = 14 cm