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?

1 Answer
Oct 15, 2015

Answer:

#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#