Question

A solid right circular cone of height 60 centimeter and radius 30 centimeter is dropped in a righy circular cylinder full of water of hieght 180 cm and radius 60 cm find volume of water left in cylinder​

Answer 1

Here is ur answer :

Given,

Height h of cone = 60 cm

Radius r of cone = 30 cm

Volume of cone

= \frac{1}{3} \pi {r}^{2} h=

3

1

πr

2

h

= \frac{1}{3} \times \pi \times {30}^{2} \times 60=

3

1

×π×30

2

×60

= \frac{1}{3} \times \pi \times 900 \times 60=

3

1

×π×900×60

= \pi \times 900 \times 20=π×900×20

= 18000\pi \: \: {cm}^{3}=18000πcm

3

____________________

For cylinder

Height h of cylinder = 180 cm

Radius r of cylinder = 60 cm

Volume of cylinder

\pi {r}^{2} hπr

2

h

= \pi \times {60}^{2} \times 180=π×60

2

×180

= \pi \times 3600 \times 180=π×3600×180

= 648000 \: \: {cm}^{3}=648000cm

3

When we drop the cone inside the cylinder which is full of water, then

Volume of water flows out = Volume of cone.

Volume of water that is left in cylinder

= Volume of cylinder — Volume of cone

= 648000 \pi - 18000\pi=648000π−18000π

= 63000\pi=63000π

= 63000 \times \frac{22}{7}=63000×

7

22

= 9000 \times 22=9000×22

= 198000 \: \: {cm}^{3}=198000cm

3

1 {cm}^{3} = {1}^{ - 6} {m}^{3}1cm

3

=1

−6

m

3

198000 \: {cm}^{3} = 0.198 \: {m}^{3}198000cm

3

=0.198m

3

Therfore,

Volume water left in the cylinder = 0.198 m³

HOPE IT HELPS YOU..

Step-by-step explanation:

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