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

Answer:

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

Step-by-step 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:

$V =\frac{4}{3}\pi r^3$

where  

r = is the radius

In the question we are given with diameter,

So

$radius = \frac{diameter}{2}$

radius = $\frac{6}{2}$

Radius = 3

We need the volume of the hemisphere

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

$\frac{V}{2} = \frac{2}{3}\pi r^3$

Thus the volume of the hemisphere is

$V =\frac{2}{3} \pi r^3$

Now substituting the values

$V = \frac{2}{3} \pi(3)^3$

$V = \frac{2}{3}\pi(27)$

$V = \frac{54 \pi}{3}$

$V = \frac{169.56}{2}$

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