Question

a fish tank in the shape of a sphere is filled with water and has a diameter of 2 feet. if water weighs 62.4 pounds per cubic feet what is the total weight of the water in a full tank to the nearest pound

Answer 1

A fish tank in the shape of a sphere is filled with water and has a diameter of 2 feet.

Recall that the volume of a sphere is given by

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

Where r is the radius.

Since the radius is half of the diameter, the formula becomes

`V=(4)/(3)\cdot\pi\cdot((D)/(2))^3`

So, the volume of the fish tank is

`\begin{gathered} V=(4)/(3)\cdot\pi\cdot((2)/(2))^3 \\ V=(4)/(3)\cdot\pi\cdot(1)^3 \\ V=(4)/(3)\cdot\pi\cdot1 \\ V=4.19\: ft^3 \end{gathered}`

The weight of the water is 62.4 pounds per cubic foot.

The total weight of the water in the fish tank can be found by multiplying the volume of the fish tank by the weight of the water.

`\begin{gathered} Total\: weight=4.19\: ft^3*62.4\: (lb)/(ft^3) \\ Total\: weight=261\: lb \end{gathered}`

Therefore, the total weight of the water in a full tank is 261 pounds. (rounded to the nearest pound)