Review question

# Can we find the centre of mass of a solid hemisphere? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5584

## Question

The region in the first quadrant enclosed by the curve $y = \dfrac{b(a^2 - x^2)^{1/2}}{a}$ and the lines $y = 0$, $x = 0$, $x = ka$ $(0 < k \le 1)$, is rotated through four right angles about the $x$-axis to form a solid of revolution. Show that the volume of the solid is $\tfrac{1}{3} \pi ab^2k(3-k^2)$.

If this solid is of uniform density find the coordinates of its centre of mass.

By considering the case $b = a$, $k = 1$, show that the centre of mass of a uniform solid hemisphere of radius $a$ is at a distance $\tfrac{3}{8}a$ from the centre.