Question

The surface area of a sphere is $616$ square cm. If its radius is changed so that the area gets reduced by $75\%$, then the radius becomes

• A. $1.6$ cm
• B. $2.3$ cm
• C. $2.5$ cm
• D. $3.5$ cm

Answer 1

The correct option is D $3.5$ cm

New area $=25\%$ of original area
$4\pi r^2=\frac{1}{4}\times 616$
$4\pi r^2=154$
$4\times \frac{22}{7}\times r^2=154$
$r^2=\frac{49}{4}={\left(\frac{7}{2}\right)}^2$
Therefore, $r=\frac{7}{2}$ or $3.5$ cm