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A solid sphere of radius R is cut into two parts at a distance of $\frac{R}{2}$ from the centre as shown in the figure. The volume of the upper part (spherical cap) is given as $\frac{n π R^{3}}{24}$ . Find the value of n.

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answer is 5.

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Detailed Solution

Taking disc element, the required volume is $\int_{R / 2}^{R} π r^{2} d y = π \int_{R / 2}^{R} (R^{2} - y^{2}) d y = \frac{5 π R^{3}}{24}$

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