Question

A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is $108cm$ and the diameter of the hemispherical ends is $36cm$, find the cost of polishing the surface of the solid at the rate of $7$ paise per sq.cm (Use $\pi =22/7$)

Answer 1

radius of the cylinder $=r_1=18cm$
height of the cylinder $h=72cm$

total surface area
$=$ curved surface are of the cylinder + surface areas of hemispherical ends

$=(2\pi rh+2\times 2\pi r^2){cm}^2=(2\pi rh+4\pi r^2){cm}^2=2\pi r(h+2r){cm}^2$

$=2\times \frac{22}{7}\times 18\times (72+36){cm}^2=12219.42{cm}^2$

Rate of polishing $7$ paise per sq.cm
Cost of polishing $=Rs.(12219.42\times \frac{7}{100})$

$=Rs.855.36Rs$