Question

A solid is in the form of a cylinder with hemispherical ends. 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.

Answer 1

Volume of solid$=\pi r^{2}h+2\times \frac{2}{3}\pi r^3$

$=\pi r^2[h+\frac{4r}{3}]=\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}[(19-7)+\frac{4\times 7}{3\times 2}]$

$=38.5(12+\frac{14}{3})=38.5\times \frac{50}{3}$

$=641.67c{m}^3$

TSA of solid$=2\pi rh+2\times 2\pi r^2=2\pi r(h+2r)$

$=2\times \frac{22}{7}\times \frac{7}{2}[(19-7)+2\times \frac{7}{2}]$

$=22(12+7)=22\times 19$

$=418c{m}^2$