Question

A circle circumscribes a rectangle with sides $16cm$ and $12cm$. What is the area of the circle?

• A. $48\pi$ square cm
• B. $50\pi$ square cm
• C. $100\pi$ square cm
• D. $200\pi$ square cm

Answer 1

The correct option is C $100\pi$ square cm

REF image

The diagonal of the rectangle is a diameter of the circle.

Now, by Pythagoras theorem

$(2r{)}^2={16}^2+{12}^2$
$=256+144$
$=400$
$={20}^2$
$\therefore r=10cm$

$Area=\pi r^2=\pi \times 10\times 10c{m}^2=100\pi c{m}^2$