Question

What is the difference in the areas of a circle with diameter 4 m and a circle with diameter 6 m? Round your answer to the nearest square meter.

a. 63 m2
b. 16 m2
c. 22 m2
d. 101 m2

Answer 1

Hi there,


Area of a circle with 4m = π(2)² = 4π m²

Area of a circle with 6m = π(3)² = 9π m²

Difference = 9π - 9π = 5π = 16 m² (nearest m²)

Answer: 16 m² (Answer B)


Hope it helps,
TF

Answer 2

Option b is correct

16
`m^2`

Explanation:

Area of circle (A) is given by:

`A = \pi r^2`

where, r is the radius of the circle.

As per the statement:

the areas of a circle with diameter 4 m

Formula for Diameter(d) is:

`d = 2r`

⇒
`4 =2r`

Divide both sides by 2 we get;

r = 2 m

then;

`A= \pi \cdot (2)^2 = 4 \pi`

It is also given: a circle with diameter 6 m

Similarly;

`6 = 2r'`

⇒
`r' = 3 m`

then;

`A' = \pi \cdot 3^2 = 9 \pi`

We have to find the difference in these areas:

`A'-A = 9 \pi -4 \pi = 5 \pi`

Use
`\pi = 3.14`

then;

`A'-A = 5 \cdot 3.14 = 15.7 m^2 \approx 16 m^2`

Therefore, the difference in the areas of a circle with diameter 4 m and a circle with diameter 6 m is,
`16 m^2`