• # question_answer A frustum of sphere is made by cutting two parallel planes of any sphere. If radius of sphere is 5 cm and distance between the plane is 1 cm, then what will be the curved surface of frustum when the distance of first plane from the centre of sphere is 2 cm              [UPSEAT 1999] A)            $5\pi \,c{{m}^{2}}$          B)            $10\pi \,c{{m}^{2}}$ C)            $15\pi \,c{{m}^{2}}$        D)            $40\pi \,c{{m}^{2}}$

Correct Answer: B

Solution :

Equation of circle is,${{x}^{2}}+{{y}^{2}}={{5}^{2}}$            $\therefore \,\,{{y}^{2}}=25-{{x}^{2}}$, $2y\frac{dy}{dx}=-2x$, $\therefore \frac{dy}{dx}=-\frac{x}{y}$ Curved surface of frustum $=2\pi \int_{2}^{3}{yds}$$=2\pi \int_{2}^{3}{y.\frac{5}{y}dx}$            $=2\pi \int_{2}^{3}{5dx}$$=2\pi [5x]_{2}^{3}=10\pi \,c{{m}^{2}}$.

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