Question

A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is $19cm$ and the diameter of the cylinder is $7cm$. find the volume and total surface area of the solid (Use $\pi =22/7$)

Answer 1

Let $r$ cm be the radius and $h$ cm the height of the cylinder. Then,

$r=\frac{7}{2}cm;h=(19-2\times \frac{7}{2})cm=12cm$
Also radius of hemisphere $=\frac{7}{2}cm=rcm$

Now,
volume of the solid = volume of the cylinder + volume of two hemisphere

$\{\pi r^{2}h+2\left(\frac{2}{3}\pi r^3\right)\}{cm}^3=\pi r^2(h+\frac{4r}{3}){cm}^3$

$=\{\frac{22}{7}\times {\left(\frac{7}{2}\right)}^2\times (12+\frac{4}{3}\times \frac{7}{2})\}{cm}^3=\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times \frac{50}{3}{cm}^3=641.66{cm}^3$

Surface area of the solid

$=$curved surface are of cylinder + surface area of two hemisphere

$=(2\pi rh+2\times 2\pi r^2){cm}^2$

$=2\pi r(h+2r){cm}^2$

$=2\times \frac{22}{7}\times \frac{7}{2}(12+2\times \frac{22}{7}\times \frac{7}{2}){cm}^2$

$=(2\times \frac{22}{7}\times \frac{7}{2}\times 19){cm}^2=418{cm}^2$