Question

What is the sector area created by the hands of a clock with a radius of 9 inches when the time is 4:00? 6.75π in.2 20.25π in.2 27π in.2 81π in.2?

Answer 1

27π in.2 is the answer

Answer 2

we know that

The area of a circle is equal to

`A=\pi r^(2)`

where

r is the radius of the circle

In this problem we have

`r=9\ in`

substitute in the formula

`A=\pi*9^(2)=81 \pi\ in^(2)`

The area of the complete circle subtends
`360\ degrees`

When the time is 4:00 the angle formed by the hands of a clock is
`120\ degrees`

so by proportion

Find the area of the sector area

`(81\pi)/(360) (in^(2))/(degree) =(x)/(120) (in^(2))/(degree) \\ \\x=120*81 \pi /360\\ \\x=27 \pi\ in^(2)`

therefore

the answer is the option

`27 \pi\ in^(2)`