Question

A solid consisting of a right circular cone of height 120 cm and radius 60cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder. If the radius of the cylinder is 60cm and its height is 180cm.


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Answer 1

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➳ Given, Radius of cone=60cm

➳ Height of cone=120cm

➳ Radius of hemisphere=60cm

➳ Radius of cylinder=60cm

➳ Height of cylinder=180cm

$Volume \: of \: cone \: \: is, \\ = \frac{1}{3} \pi {r}^{2} h \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \frac{1}{3} \pi \times {660}^{2} \times 120 \\ = 14000\pi {cm}^{3}$

$Volume \: of \: hemisphere \: is,</p><p> \\=\frac{4}{3} π {r}^{3} h\\= \frac{2}{3} \pi {60}^{3} h \: \: \: \: \: \: \: \: \: \: \\ = 144000\pi {cm}^{3}$

$Volume \: of \: cylinder \: is, \\ = \pi {r}^{2} h \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \pi \times {60}^{2} \times 180 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 648000\pi {cm}^{3}$

$Volume \: of \: water \: left \: in cylinder \: is \\ \: \: \: \: \: \: \: \: \: \: \: = \pi {r}^{2} h - \frac{1}{3} \pi {r}^{2} h - \frac{4}{3} \pi {r}^{3} h \\ = (648000−288000)π \\ =360000π \\ \: \: \: \: \: \: \: {=1130400cm}^{3}$

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