If the radius of a sphere is increased by 2 cm, then its surface area increases by 352 cm². The radius of the… · ABC26GN5001

Subject: General Aptitude · Chapter: Volume and Surface Area

If the radius of a sphere is increased by 2 cm, then its surface area increases by $352 \mathrm{cm}^{2}$. The radius of the sphere before the increase was

(a)3 cm

(b)4 cm

(c)5 cm

(d)6 cm

Answer

Answer (as printed): D

Explanation

$4 \pi(r+2)^{2}-4 \pi r^{2}=352 \Leftrightarrow(r+2)^{2}-r^{2}=\left(352 \times \frac{7}{22} \times \frac{1}{4}\right)=28$. $$\begin{aligned} & \Leftrightarrow(r+2+r)(r+2-r)=28 \quad \Leftrightarrow \quad 2 r+2=14 \\ & \Rightarrow \quad r=\left(\frac{14}{2}-1\right)=6 \mathrm{cm} . \end{aligned}$$

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