Question

The sum of the radius of base and height of a solid right circular cylinder is 37 cm . If the total surface area of the solid cylinder is 1628 cm² , find the volume of cylinder. (Use $\mathrm{\pi }=$22 / 7 )

Answer 1

Let the radius of the base of the cylinder be r cm
Let the height be h cm.
Now given that r + h = 37 cm
Total surface area = 1628 cm² ...(i)
$$\begin{gathered} Totalsurfaceareaofthecylinder=2{\mathrm{\pi r}}^2+2\mathrm{\pi rh} \\ =2\mathrm{\pi r}\left(\mathrm{r}+\mathrm{h}\right) \\ =2\mathrm{\pi r}\times 37 \\ =74\mathrm{\pi r}...\left(\mathrm{ii}\right) \end{gathered}$$
From equation (i) and (ii) we get
$$\begin{gathered} 74\mathrm{\pi r}=1628 \\ \Rightarrow \mathrm{r}=\frac{1628}{74\mathrm{\pi }}=7{\mathrm{cm}}^3 \end{gathered}$$
Thus, the height will be 37 − 7 = 30 cm
Thus, the volume of the cylinder = ${\mathrm{\pi r}}^2\mathrm{h}=\mathrm{\pi }{\left(7\right)}^2\times 30=4620{\mathrm{cm}}^3$
Hence the volume is 4620 cm³