Question

A hemispherical tank is filled with water and has a diameter of 20 feet. If water weighs 62.4 pounds per cubic foot, what is the total weight of the water in a full tank, to the nearest pound?

Answer 1

Answer:

Step-by-step explanation:

Given :-

Diameter of tank = 20 feet

Radius of tank, r = 20/2 = 10 feet

To Find :-

Volume of the hemisphere

Formula to be used :-

Volume of the hemisphere = 2/3 × π × r³

Solution :-

Putting the values, we get

Volume of the hemisphere = 2/3 × π × r³

⇒ Volume of the hemisphere = 2/3 × 22/7 × 10 × 10 × 10

⇒ Volume of the hemisphere = 44000/21

⇒ Volume of the hemisphere = 2095. 23 feet³

Now, Total weight of the water

⇒ Total weight of the water = 62.4 × 2095.23

⇒ Total weight of the water = 130742.35 pounds

Hence, the Total weight of the water is 130742.35 pounds.

Answer 2

Aɴꜱᴡᴇʀ

Weight of water = 130742

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Gɪᴠᴇɴ

➳ Diameter of the tank = 20 feet

➳ Weight of water = 62.4 pounds per cubic feet

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Tᴏ ꜰɪɴᴅ

➠ Weight of water when tank is full?

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Sᴛᴇᴘꜱ

❍ Volume of a hemisphere is given by,

$\underline{ \boxed{ \sf{} \red{\frac{2}{3}\pi {r}^{3} }}}$

For that we need the radius which is equal to 20/2 = 10 feet

Substituting the given values,

$\leadsto \sf\frac{2}{3} \times \frac{22}{7} \times {10}^{3} \\ \\ \leadsto \sf \pink{2095.23 \: {m}^{3} }$

So now weight of water is the product of the volume with the weight of water,

➤ 2095.23 × 62.4 = 130742.35 Pounds

Rounding off to the nearest pound your answer becomes,

Weight of water = 130742 Pounds

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