Question

A solid is consisting of right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm. It 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.(use
$\pi = 3.14$
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Answer 1

Given:-

• Radius of cone=60cm
• Height of cone=120cm
• Radius of hemisphere=60cm
• Radius of cylinder=60cm
• Height of cylinder=180cm

To Find:-

• the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.

step-by-step solution:-

volume of cylinder = πr²h

• → $\sf\frac{22}{7}$ × (60)² × 180

• → $\sf\frac{22 × 3600 × 180}{7}$

• → $\sf\frac{14256000}{7}$cm³

Volume of solid = Volume of cone + Volume of hemisphere

• → $\sf\frac{1}{3}$ × $\sf\frac{22}{7}$ × (60)² × 120 + $\sf\frac{2}{3}$ × $\sf\frac{22}{7}$ × 60³

• $\sf\frac{3168000}{7}$ + $\sf\frac{3168000}{7}$ = $\sf\frac{6336000}{7}$cm³

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

• → $\sf\frac{14256000}{7}$ - $\sf\frac{6336000}{7}$ = $\sf\frac{7920000}{7}$

• → 1131428.57142

• → 1.131m³

Answer 2

Answer:

Volume of Water left in Cylinder = 1131428.57 cm³

Step-by-step explanation:

Given :

Height of Cone, h = 120 cm

Radius of Cone, r = 60 cm

Radius of Hemisphere, r = 60 cm

Height of Cylinder, H = 180 cm

Radius of Cylinder, r = 60 cm

To Find :

Volume of water left in cylinder.

Solution :

We know that :

Volume of water left in cylinder :

$\bigstar\;\boxed{\textsf {Volume of cylinder - (Volume of cone + Colume of the hemisphere)}}}$

Values in Equation :

⇒ πr² H - ($\dfrac{1}{3}$ πr²h + $\dfrac{2}{3}$ πr³)

⇒ πr² (H - ([/tex]$\dfrac{1}{3}$ h + $\dfrac{2}{3}$ πr))

⇒ $\dfrac{22}{7}$ × 60² (180 - ($\dfrac{1}{3}$ 120 + $\dfrac{2}{3}$ 60))

⇒ $\dfrac{22}{7}$ × 3600(180 - (40 + 40))

⇒ $\dfrac{22}{7}$ × 3600 × 100

⇒ 1131428.57 cm³

∴ Volume of Water left in Cylinder = 1131428.57 cm³