Question

The perimeter of a semi-circular metallic plate is 86.4 cm. Calculate the radius and area of the plate.

• A. 16.8 cm, 424.52 $c{m}^2$
• B. 12.8 cm, 424.52 $c{m}^2$
• C. 16.8 cm, 443.52 $c{m}^2$
• D. 12.8 cm, 443.52 $c{m}^2$

Answer 1

The correct option is C 16.8 cm, 443.52 $c{m}^2$

Perimeter of a semi circular plate $=\pi r+2r$
Given, $\pi r+2r=86.4$
$=>r(\pi +2)=86.4$
$=>r=\frac{86.4}{\pi +2}$
$=>r=\frac{86.4}{\frac{22}{7}+2}$
$=>r=\frac{86.4}{\frac{36}{7}}$
$=>r=\frac{86.4\times 7}{36}$
$=>r=16.8$ cm
Area of a semi circle $=\frac{\pi r^2}{2}$
$=\frac{22\times {16.8}^2}{7\times 2}$
$=443.52c{m}^2$