Question

A water tank is hemispherical below and cylindrical at the top. If the radius is 1212 m and capacity is 3312π3312π cubic metre, the height of the cylindrical portion in metres is:
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Answer 1

Correct question, A water tank is hemispherical below and cylindrical at the top. If the radius is 12 m and capacity is 3312π cubic metre

• To find, Height of cylinder in meter

Solution :

★ Radius of water tank = 12 m

★ Capacity of water tank = Volume of water tank = 3312π m³

• Volume of hemisphere

→ ⅔ πr³

→ ⅔ × π × 12 × 12 × 12

→ 2 × π × 4 × 12 × 12

→ 8 × 144 × π

→ 1152 πm³

•°• Volume of hemisphere is 1152 πm³

★ Volume of hemisphere + Volume of cylinder = Volume of water tank

→ Volume of cylinder = Volume of water tank - Volume of hemisphere

→ πr²h = 3312 π - 1152 π

→ π × 12 × 12 × h = 2160 π

• Cancel π

→ 12 × 12 × h = 2160

→ 144 h = 2160

→ h = 2160/144

→ h = 15 m

•°• Height of cylinder in meter is 15m

Answer 2

Answer:

Appropriate Question :-

• A water tank is hemispherical below and cylindrical at the top. If the radius is 12 m and the capacity is 3312π cubic metre. Find the height of the cylindrical portion in metres.

Given :-

• A water tank is hemispherical below and cylindrical at the top. The radius is 12 m and the capacity is 3312π cubic metre.

To Find :-

• What is the height of the cylindrical portion in metres.

Formula Used :-

$\clubsuit$ Volume of Hemisphere Formula :

$\longmapsto \sf\boxed{\bold{\pink{Volume_{(Hemisphere)} =\: \dfrac{2}{3}{\pi}r^3}}}$

$\clubsuit$ Volume of Cylinder Formula :

$\longmapsto \sf\boxed{\bold{\pink{Volume_{(Cylinder)} =\: {\pi}r^2h}}}$

where,

• r = Radius
• h = Height

Solution :-

First, we have to find the volume of hemisphere :

Given :

• Radius = 12 cm

According to the question by using the formula we get,

$\implies \sf Volume_{(Hemisphere)} =\: \dfrac{2}{3} \times {\pi} \times {(12)}^{2}$

$\implies \sf Volume_{(Hemisphere)} =\: \dfrac{2}{3} \times {\pi} \times 1728$

$\implies \sf Volume_{(Hemisphere)} =\: \dfrac{\cancel{3456}}{\cancel{3}} \times {\pi}$

$\implies \sf Volume_{(Hemisphere)} =\: \dfrac{1152}{1} \times {\pi}$

$\implies \sf\bold{\green{Volume_{(Hemisphere)} =\: 1152{\pi}\: m^2}}$

Hence, the volume of hemisphere is 1152π m².

Now, we have to find the height of the cylindrical portion :

As we know that :

$\bigstar$ The total capacity of the tank = Capacity of hemispherical portion + Capacity of Cylindrical portion $\bigstar$

Given :

• Radius = 12 cm
• Volume of Hemisphere = 1152π m²

According to the question by using the formula we get,

$\longrightarrow \sf 1152{\pi} + {\pi}r^2h =\: 3312{\pi}$

$\longrightarrow \sf {\pi}r^2h =\: 3312{\pi} - 1152{\pi}$

$\longrightarrow \sf {\pi}r^2h =\: 2160{\pi}$

$\longrightarrow \sf {\pi} \times (12)^2 \times h =\: 2160{\pi}$

$\longrightarrow \sf {\cancel{{\pi}}}144h =\: 2160{\cancel{{\pi}}}$

$\longrightarrow \sf 144h =\: 2160$

$\longrightarrow \sf h =\: \dfrac{\cancel{2160}}{\cancel{114}}$

$\longrightarrow \sf h =\: \dfrac{15}{1}$

$\longrightarrow \sf\bold{\red{h =\: 15\: m}}$

$\therefore$ The height of the cylindrical portion is 15 m .