Question

From a solid cylinder of height $4cm$ and radius $3cm$, a conical cavity of height $4cm$ and of base radius $3cm$ is hollowed out. What is the total surface area of the remaining solid?

• A. $15\pi$ square cm
• B. $22\pi$ square cm
• C. $33\pi$ square cm
• D. $48\pi$ square cm

Answer 1

The correct option is D $48\pi$ square cm

$l=\sqrt{3^2+4^2}=5$
Total surface area of remaining solid
$=CSA$ of cone $+CSA$ of cylinder $+$ area of base of cylinder
$=\pi rl+2\pi rh+\pi r^2$
$=\pi r(l+2h+r)$
$=\pi \times 3\times (5+2\times 4+3)$
$=\pi \times 3\times 16$
$=48\pi c{m}^2$