Question

MATHS "CLASS - X"

SURFACE AREAS AND VOLUMES

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.

Excercise 13.2
7th Question

Answer 1

hey Frnd.....
Radius of cone = 60 cm, height of cone = 120 cm

Radius of hemisphere = 60 cm

Radius of cylinder = 60 cm, height of cylinder = 180 cm

Volume of cone

= (1)/(3)πr^2h

=(1)/(3) πxx60^2xx120

=144000π cm^3

Volume of hemisphere

=(2)/(3) πr^3

=(2)/(3) πxx60^3

=144000π cm^3

Volume of solid

=(144000+144000) π=288000π cm^3`

Volume of cylinder

=πr^2h
=πxx60^2xx180
=648000π cm^3

Volume of water left in the cylinder

=(648000+288000) π=1130400 cm^3

HOPE THIS HELPS YOU ☺ ☺ ❤ ❤ ❤

Answer 2

Here's the answer

In cylinder,

Radius = r = 60 cm
Height = h = 180 cm

Volume of cylinder (outer cylinder) = ?

${\boxed {\boxed {\sf{Volume \: of \: Cylinder = \pi \: r {}^{2} h}}}}$

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

$\sf{ = \frac{22}{7} \times 3600 \times 180}$

$\sf{= \frac{22}{7} \times 648000}$

$\sf{ = 22 \times 92571}$

$\sf{ = 2,036,562 \: cm {}^{3} }$

Volume of cylinder (outer cylinder) = 2,036,562 cu. cm

Now,

Volume of cone = ?

Radius = r = 60 cm
Height = h = 120 cm

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

$\sf {= \frac{{1} }{3} \times \frac{22}{7} \times 60 {}^{2} \times 120}$

$\sf{= \frac{1}{3} \times \frac{22}{7} \times 3600 \times 120}$

$\sf{ = 1 \times \frac{22}{7} \times 3600 \times 40}$

$\sf {= \frac{22}{7} \times 14400}$

$\sf {= \frac{3168000}{7}}$

$\sf{ = 452751 \: cm {}^{3} }$

Now,

Volume of hemisphere = ?

Radius = r = 60 cm

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

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

$\sf {= \frac{2}{3} \times \frac{22}{7} \times 60 \times 60 \times 60} \\ \\ \sf{ = 2 \times \frac{22}{7} \times 20 \times 60 \times 60}$

$\sf{=2 \times \frac{22}{7} \times 72000}$

$\sf{= 44 \times 10285.71}$

$\sf{ = 452751 \: cm {}^{3} }$

Therefore,

Volume of Cone + Volume of hemisphere = Volume of solid

$\sf{452 , 751 + 452 , 751 =905502}$

905,502 cu. cm = Volume of the solid

Now,

We have to find Volume of water left in cylinder

Volume of water left in cylinder = Volume of Cylinder - Volume of solid

$\sf{= 2,036,562 - 905,502}$

$\sf{= 1,131,060} \: cm {}^{3}$

$\sf{ \approx \: 1.131.0\: m {}^{3}}$

Therefore ,

Volume of the water left in the cylinder is 1.131 cu.m

_______________________________

Thanks !!