A napkin-holder is formed by boring a cylindrical hole, of length $2h$, through a wooden sphere of r

Question

A napkin-holder is formed by boring a cylindrical hole, of length $2h$, through a wooden sphere of radius $a$, where $a$ is a fixed constant. The axis of the hole passes through the centre $O$ of the sphere. The diagram shows a cross-section through $O$, with $x$- and $y$-axes taken parallel and perpendicular to the axis of the hole respectively. Let $V$ denote the volume of the wood forming the napkin-holder. By considering the napkin-holder as a solid of revolution about the $x$-axis, find $V$ in terms of $h$, verifying that it is independent of $a$. [4]

Accepted Answer

$V=\frac{4}{3}\pi {{h}^{3}}$

2019 TJC Promo Q7

2019 TJC Promo Q7

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