Question

A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 98 cm and the diameter of each of its hemispherical ends is 28 cm, find the cost of polishing the surface of the solid at the rate of 15 paise per sq cm.

Answer 1

The arrangement is shown in the figure:



Diameter of the cylinder = 28 cm
Therefore, radius of the cylinder = Radius of the hemispheres= 14 cm

Surface area of two hemispheres$=2\times 2{\mathrm{\pi r}}^2=2\times 2\times \frac{22}{7}\times 14\times 14=2464{\mathrm{cm}}^2$

Length of cylinder $=98-14\times 2=98-28=70cm$

Curved surface area of cylinder $=2\mathrm{\pi rl}=2\times \frac{22}{7}\times 14\times 70=6160{\mathrm{cm}}^2$

Total surface area$=2464+6160=8624c{m}^2$

Cost of polishing the entire object$=8624\times 15=129360\text{paise}=\text{Rs}1293.60$