Question 855997
of the tank is (x - 3) feet, the expression below shows the volume of the tank.

1 over 3π (x - 7)^2 (x - 3)

What does the factor π(x - 7)^2 (x - 3) represent?

A.The area of the base of the tank

B.The area of the curved sides of the tank

C.The volume of 3 of the same cone-shaped tanks

D.The volume of 6 of the same cone-shaped tanks 




Volume of a cone is given by the formula {{{(1/3) pir^2h}}}

r is the radius and h is the height

The expression for volume is{{{( 1/3)pi (x - 7)^2 (x - 3)}}}

compare the two equations

r^2= (x-7)^2 so r= (x-7)

h= (x-3 ) given

A. The area of base of tank = {{{pi r^2}}}

so The area of base = {{{pi (x-7)^2}}}

B. The slant height is {{{ sqrt(r^2+h^2)}}}

slant height = {{{ sqrt((x-7)^2+(x-3)^2)}}}

= {{{ sqrt(x^2-14x+49 +x^2-6x+9)}}}

={{{sqrt(2x^2-20x+58)}}}


curved surface area = pi r l

= {{{pi * (x-7)*sqrt(2x^2-20x+58)}}}


Volume of 3 tanks is three times