Question

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to its and the height of the cone is equal to its radius. Find the volume of the solid in terms of π.​

Answer 1

$\\ \\ \large\underline{ \underline{ \sf{ \red{given:} }}}$

• Radii of cone and hemisphere are same.

• Radii is equal to the height of cone.

$\\ \\ \large\underline{ \underline{ \sf{ \red{to \: find:} }}}$

• Volume of the solid [ cone + hemisphere ]

$\\ \\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

• Volume of solid = Volume of cone

ㅤㅤㅤㅤㅤ+ Volume of hemisphere

$\\ \\ \bigstar\boxed{ \bf \:volume \: of \: cone = \frac{1}{3}\pi \: {r}^{2} h }$

We know , height = radius = r

$\\ \\ \bigstar \boxed{ \bf \:volume \: of \: hemisphere = \frac{2}{3} \pi \: {r}^{3} }$

$\\ \\ \sf \: volume \: of \: solid = \frac{1}{3} \pi {r}^{2} h \: + \frac{2}{3} \pi \: {r}^{3} \\ \\ \\ \sf \: volume \: of \: solid = \frac{1}{3} \pi {r}^{2} (r) + \frac{2}{3} \pi {r}^{3} \\ \\ \\ \sf \: volume \: of \: solid = \frac{1}{3} \pi {r}^{3} + \frac{2}{3} \pi {r}^{3} \\ \\ \\ \sf \: volum e\: of \: solid = \frac{\pi {r}^{3} + 2\pi {r}^{3} }{3} \\ \\ \\ \sf \: volume \: of \: solid = \frac{3\pi {r}^{3} }{3} \\ \\ \\ \underline{\boxed { \sf \: \orange{volume \: of \: solid = \pi {r}^{3} }}}$

Hence , volume of solid is πr³.

__________________ㅤㅤㅤ

ㅤㅤㅤㅤㅤ

More to know :-

• Volume of cube = edge³

• Volume of cuboid = 2(lh+bh+lb)

• Volume of cylinder = πr²h

• Volume of sphere = (4/3)πr³