Question

If the total surface area of a solid right circular cylinder is $880sq.cm$ and its radius if $10cm$, find its curved surface area. (Take $\pi =\frac{22}{7}$)

Answer 1

Let $r$ and $h$ be the radius and height of the solid right circular cylinder respectively.
Let $S$ be the total surface area of the solid right circular cylinder.
Given that $r=10cm$ and $S=880{cm}^2$
Now, $S=880$ $\Rightarrow 2\pi r[h+r]$
$2\times \frac{22}{7}\times 7\times 10(h+10)=880$
$\Rightarrow h+10=\frac{880\times 7}{2\times 22\times 10}$
$\Rightarrow$ $h+10=14$
Thus, the height of the cylinder, $h=4cm$
Now, the curved surface area, $CSA$ is
$2\pi rh=2\times \frac{22}{7}\times 10\times 4=\frac{1760}{7}$
Thus, the curved surface area of the cylinder $=251\frac{3}{7}sq.cm.$