Question

7. A solid consisting of a right circular cone of height 120 cm and radius 60 cm 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 60 cm and its height is 180 cm.
​

Answer 1

Answer:

$\bold{Volume \: of \: water \: left \: in \: cylinder}$

$\bold{=Volume \: of \: cylinder- Volume \: of \: solid}$

$\bold \pink{Volume \: of \: cylinder }$

$\bold\pink{radius = r = 60cm}$

$\bold\pink{ height = h = 180cm}$

$\bold \pink{Volume \: of \: outer \: cylinder = \pi {r}^{2}h }$

$\bold \pink{ = \frac{22}{7} \times ({60})^{2} \times 180}$

$\bold \pink{ = \frac{14256000}{7} {cm}^{3} }$

$\bold \red{Volume \: of \: solid}$

$\bold \red{Volume \: of \: solid =Volume \: of \: cone + Volume \: of \: hemisphere}$

$\bold\red{ \underline{Volume \: of \: cone}}$

$\bold \red{radius = r = 60cm}$

$\bold \red{height = h = 120cm}$

$\bold \red{Volume \: of \: cone = \frac{1}{3}\pi {r}^{2} h}$

$\bold \red{ = \frac{1}{3} \times \frac{22}{7} \times ( {60})^{2} \times 12}$

$\bold \red{ = \frac{316800}{7} {cm}^{3} }$

$\bold \green{ \underline{Volume \: of \:hemisphere}}$

$\bold \green{radius = r = 60cm}$

$\bold \green{Volume \: of \: hemisphere = \frac{2}{3}\pi {r}^{3} }$

$\bold \green{ = \frac{2}{3} \times \frac{22}{7} \times {60}^{3} }$

$\bold \green{ = \frac{3168000}{7} {cm}^{3} }$

Hence,

Volume of solid =Volume of cone+Volume of Cylinder

$\bold{ \frac{316800}{7} + \frac{3168000}{7} {cm}^{3} }$

$\bold{ = \frac{6336000}{7} cm {}^{ 3} }$

Now,

Volume of water left in cylinder

$\bold{Volume \: of \: cylinder -Volume \: of \: solid}$

$\bold{= \frac{14256000}{7} - \frac{6336000}{7} }$

$\bold{ = \frac{14256000 - 633600}{7} }$

$\bold{ = (\frac{7920000}{7} )cm {}^{3} }$

$\bold{ = 1131428.57 {cm}^{3 } }$

$\bold{ = 1131428.57 \times \frac{1}{100} {m}^{3} }$

$\bold{ = 1131428.57 \times \frac{1}{100} \times \frac{1}{100} \times \frac{1}{100} cm}$

$\bold{ = 1.131 {m}^{3} (approx)}$

Step-by-step explanation:

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