Answer:
Exact: [tex] 11 \pi~in.^2 [/tex]
Approximate: [tex] 34.6~in.^2 [/tex]
Step-by-step 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.
[tex] A_{circle} = \pi r^2 [/tex]
Larger clock, r = 6 in.
[tex]A_{large~clock} = \pi \times (6~in.)^2 = 36 \pi ~in.^2 = 113.1~in.^2[/tex]
Smaller clock, r = 5 in.
[tex]A_{small~clock} = \pi \times (5~in.)^2 = 25 \pi ~in.^2 = 78.5~in.^2[/tex]
Difference in areas:
Exact: [tex] 36 \pi~in.^2 - 25 \pi~in.^2 = 11 \pi~in.^2 [/tex]
Approximate: [tex] 113.1~in.^2 - 78.5~in.^2 = 34.6~in.^2 [/tex]
