Question

A gas tank has ends that are hemispheres of radius r ft. the cylindrical midsection is 6 ft long. express the volume of the tank as a function of r?

Answer 1

`v_("all") (ft^3)= (6pir^2 + 4/3 pi r^3) ft^3`

Explanation:

Let volume be v then:
Given: radius is r
Let length of cylinder be L

Volume of two ends when put together form a sphere
`v_("sphere") = 4/3 pi r^3` ........ ( 1 )

Volume of cylinder is circle area times length of cylinder
`v_("cylinder")= pi r^2 L`
But `L` = 6 (feet) giving
`v_("cylinder")= 6pi r^2` ........ ( 2 )

Both r and L are both measured in feet. so you can add the volumes directly, giving:

Putting the two together: ( 1 ) + ( 2 )

`v_("all")= 6pir^2 + 4/3 pi r^3`

Let feet be ft
`v_("all") (ft^3)= (6pir^2 + 4/3 pi r^3) ft^3`