Question

Circumference of a circle is 66 in and the radius is $10.5$ in. The approximate value of $\pi$ is _____ and the area of the circle to the nearest tenth is _______ sq in, if the area is given by the expression $110.25\pi$ in${}^2$.

Answer 1

Circumference of the circle $=66$ in
Radius of the circle $=10.5$ in
Formula to find the circumference of the circle $=2\times \pi \times r$
Considering the formula, $2\times \pi \times 10.5=66$
$\Rightarrow \pi \times 21=66$
$\Rightarrow \pi =\frac{66}{21}$ (Dividing bot $66$ and $21$ by $3$)
$\Rightarrow \pi =\frac{22}{7}$
Given that the area of a circle $=110.25\pi {\text{in}}^2$
So, the area of the circle will be $=\frac{22}{7}\times 110.25$
$=\frac{2425.5}{7}=346.5$ sq in
So, option A is the correct answer.