Question

A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 105 cm and the diameter of the hemispherical ends is 36 cm each, find the cost of polishing the surface of the solid at the rate of 21 paise per square cm. [4 MARKS]

Answer 1

Formula Framing: 2 Marks
Application: 1 Mark
Solution: 1 Mark
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Radius, r = 18 cm for cylinder and hemisphere as well
For cylinder: h = 105 - (18 + 18= 69 cm
$\therefore$ Total surface area to be polished = Curved surface area of hemispherical end
+ Curved surface area of cylinder
+ Curved surface area of other hemispherical end
$=2\pi r^2+2\pi rh+2\pi R^2=2\pi rh+4\pi r^2=2\pi r(h+2r)=2\times \frac{22}{7}\times 18\times (69+36)=1180c{m}^2$
$\therefore$ Cost of polishing the surface of the solid = $(21\times 11880)$ paise = Rs. 2494.80