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 …

Question

asked Mar 17, 2021 51.6k views

2 Answers

Adam Harkus · Answer 1 · 2021-03-22T06:16:27+0000

Answer:

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