Question

The circumference of a circle is 64π.Then the area of the same circle is:
(A) 604π cm² (B) 1024π cm²

(C) 1050π cm² (D) 512π cm²

Answer 1

circumference of circle =64pi

2pi r =64pi

r=32

$area \: of \: circle \: = \pi {r}^{2} = \pi {32}^{2} = 1024\pi$

Answer 2

The area of circle with given circumference is 1024π $\mathrm{cm}^{2}$ Hence Option B is correct

Solution:

Given that circumference of circle = $64\pi$

We need to determine area of circle

The circumference of circle with radius "r" is given as:

$\text { Circumference of the circle }=2 \pi r$

$\begin{array}{l}{64 \pi=2 \pi r} \\\\ {2 r=64} \\\\ {r=32}\end{array}$

Hence radius "r" = 32 cm

The area of circle with radius "r" is given as:

$\text { area of the circle }=\pi r^{2}$

$\text { Area of the circle }=\pi \times(32)^{2}=1024 \pi$

Hence, the option B is correct

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