Question

Katlin is choosing between two circular wall clocks one has the radius of 5 inches while the other one has a radius of 6 inches.How much more wall space will the clock with a radius of 6 inches cover?

Plz help i dont get any of these type of questions T-T

Answer 1

Exact:
`11 \pi~in.^2`

Approximate:
`34.6~in.^2`

Explanation:

The spaces the clocks occupy on the wall are the areas of the clocks.

The clocks are shaped like circles, so use the formula for the area of a circle to find the two areas. Then subtract the smaller area from the larger area.

`A_(circle) = \pi r^2`

Larger clock, r = 6 in.

`A_(large~clock) = \pi * (6~in.)^2 = 36 \pi ~in.^2 = 113.1~in.^2`

Smaller clock, r = 5 in.

`A_(small~clock) = \pi * (5~in.)^2 = 25 \pi ~in.^2 = 78.5~in.^2`

Difference in areas:

Exact:
`36 \pi~in.^2 - 25 \pi~in.^2 = 11 \pi~in.^2`

Approximate:
`113.1~in.^2 - 78.5~in.^2 = 34.6~in.^2`