Question

a solid right circular cone of height 60 cm and radius 30 cm is dropped in a right circular cylinder full of water of height 180 cm and radius 60 cm find the volume of water left in the cylinder in cubic metres

Answer 1

Hlo friend.. Cutiepie Here..

Here is ur answer :

Given,

Height h of cone = 60 cm

Radius r of cone = 30 cm

Volume of cone

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


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


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


$= \pi \times 900 \times 20$


$= 18000\pi \: \: {cm}^{3}$
____________________

For cylinder

Height h of cylinder = 180 cm

Radius r of cylinder = 60 cm

Volume of cylinder

$\pi {r}^{2} h$


$= \pi \times {60}^{2} \times 180$


$= \pi \times 3600 \times 180$


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


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

$= 648000 \pi - 18000\pi$

$= 63000\pi$


$= 63000 \times \frac{22}{7}$


$= 9000 \times 22$

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

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

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



Therfore,

Volume water left in the cylinder = 0.198 m³


HOPE IT HELPS YOU..

REGARDS
@sunita

Answer 2

Answer 1.98 m³

Step-by-step explanation:

volume of water:Volume of cylinder-Volume of cone

-π × R²H- 1/3 × π ×r²h

- π (R²H- 1/3 r²h)

- π (60×60×180- 1/3 x 30×30×60)

- π (3600 × 180-18000)

- π × 180 (3600-100)

-22/7 × 180 × 3500

-22 × 180 × 500

-1980000 cm³

-1980000 × 10⁻⁶ m³

-1.98 m³