Question

The curved surface area of the cylinder is $1760c{m}^2$ and its volume is $24640c{m}^2$. Find its height.

Answer 1

Given that,

The curved surface area of cylinder $=1760c{m}^2$

The volume of cylinder$=24640c{m}^3$

Height of cylinder $h=?$.

We know that

The curved surface area of cylinder $=2\pi rh=1760\Rightarrow \pi rh=880$

The volume of cylinder $=\pi r^{2}h=24640$

$\Rightarrow \pi r²h=24640$

$\Rightarrow \pi rh\times r=24640$

$\Rightarrow 880\times r=24640$

$\Rightarrow r=28cm$

Now,

putting the value of ${}^{\prime }{r}^{\prime }$ in $2\pi rh=1760$

$\Rightarrow 2\pi \times 28\times h=1760$

$\Rightarrow h=\frac{1760}{56\pi }$

$\Rightarrow h=\frac{1760}{56}\times \frac{7}{22}$

$\Rightarrow h=10cm$

Hence the height is $10cm.$