Question

A hemispherical tank is filled with water and has a diameter of 6 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

3529

Explanation:

If you are here from delta math this is the Answer

Answer 2

The total weight of the water in a full tank, to the nearest pound is 3527 pounds per cubic foot

Explanation:

Given:

Diameter of the hemispherical tank = 6 feet

Weight of water per cubic foot = 62. 4 pounds

To Find:

The total weight of the water in a full tank, to the nearest pound?

Solution:

We know that the volume of a sphere is:

`V =(4)/(3)\pi r^3`

where

r = is the radius

In the question we are given with diameter,

So

`radius = (diameter)/(2)`

radius =
`(6)/(2)`

Radius = 3

We need the volume of the hemisphere

So the volume of the hemisphere will be half of the volume of teh sphere

`(V)/(2) = (2)/(3)\pi r^3`

Thus the volume of the hemisphere is

`V =(2)/(3) \pi r^3`

Now substituting the values

`V = (2)/(3) \pi(3)^3`

`V = (2)/(3)\pi(27)`

`V = (54 \pi)/(3)`

`V = (169.56)/(2)`

V= 56.52 cubic foot

Now, the total weight of water of:

W = 56.52 x 62.4

W= 3526.848 pounds per cubic foot

To the nearest pounds

W= 3527 pounds per cubic foot