Question

TSA of a solid right circular cylinder is 1540 cm². If height is 4 times of the base then find the height of cylinder.

Answer 1

Let r = radius of the base of cylinder
Let h = height of the cylinder
Now, height of cylinder = 4 (radius of base of cylinder)
so, h = 4 r .....(1)
$\mathrm{TSA}=1540c{m}^2$
$$\begin{gathered} \Rightarrow 2\mathrm{\pi }r(h+r)=1540 \\ \Rightarrow 2\times \frac{22}{7}\times r(4\mathrm{r}+r)=1540(\mathrm{using}(1\left)\right] \\ \Rightarrow r\left(5r\right)=\frac{1540\times 7}{2\times 22} \\ \Rightarrow 5r^2=35\times 7 \\ \Rightarrow r^2=49 \\ \Rightarrow r=7\mathrm{cm} \end{gathered}$$

Now h = 4r = 4(7) = 28 cm
So, height of cylinder = 28 cm