Question 855997
The volume of the tank is given by
{{{(1/3)pi(x - 7)^2 (x - 3) }}}
If you multiply that expression times 3, you get
{{{pi(x - 7)^2 (x - 3)}}} , which would be 3 times the volume of the tank,
which is the same as the sum of the volumes of 3 of the same cone-shaped tanks.
The answer is {{{highlight(C)}}} .
 
Very strange way to confuse you while trying to find out if you can multiply a strange algebraic expression times 3.
 
On the other hand, the expression is correct.
If the height is {{{x-3}}} feet, and the radius is 4 feet less than that,
the radius (in feet) is {{{x-4-3=x-7}}} .
Then, the surface area of the circular base would be
{{{pi*radius^2=pi(x - 7)^2}}} square feet.
The volume of a cone with base area {{{A}}} and height {{{h}}} is {{{(1/3)Ah}}} ,
so for our cone, the volume (in cubic feet) is indeed
{{{(1/3)pi(x - 7)^2 (x - 3) }}} .