Question

Find the circumference and area of a circle with a diameter of 10 inches. Leave your answers in terms of pi. (4 points)

A.C = 5π; A = 20π

b.C = 10π; A = 20π

c.C = 10π; A = 25π

d.C = 5π; A = 25π

which one is the right answer?

Answer 1

d=10 a=5
5×5×π=25π
a=25π
2×5×π=10π
c=10π

c. C = 10π A = 25π

Answer 2

The circumference of a circle is
`10\pi\ inches` and the area of a circle is
`25\pi\ inches^(2)` .

Option (c) is correct .

Explanation:

Formula

`Area\ of\ a\ circle = \pi r^(2)`

`Circumference\ of\ a\ circle = 2\pi\ r`

Where r is the radius of a circle .

As given

Diameter is 10 inches.

`Radius = (Diameter)/(2)`

`Radius = (10)/(2)`

Radius = 5 inches

Put values in the above formulas .

`Area\ of\ a\ circle = \pi 5^(2)`

`Area\ of\ a\ circle = \pi* 5* 5`

`Area\ of\ a\ circle = 25\pi\ inches^(2)`

`Circumference\ of\ a\ circle = 2\pi\ 5`

`Circumference\ of\ a\ circle = 2\pi* 5`

`Circumference\ of\ a\ circle = 10\pi\ inches`

Therefore the circumference of a circle is
`10\pi\ inches` and the area of a circle is
`25\pi\ inches^(2)` .

Option (c) is correct .