SOLUTION: The radius of a cone-shaped tank is 4 feet less than its height. If the height of the tank is (x - 3) feet, the expression below shows the volume of the tank. 1 over 3π (x

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Question 855997: The radius of a cone-shaped tank is 4 feet less than its height. If the height 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

I want to understand this problem with detail, why the correct answer is the correct and how that is correct?

Found 2 solutions by mananth, KMST:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
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
r is the radius and h is the height
The expression for volume is
compare the two equations
r^2= (x-7)^2 so r= (x-7)
h= (x-3 ) given
A. The area of base of tank =
so The area of base =
B. The slant height is
slant height =
=
=

curved surface area = pi r l
=

Volume of 3 tanks is three times




Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
The volume of the tank is given by

If you multiply that expression times 3, you get
, 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 .

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 feet, and the radius is 4 feet less than that,
the radius (in feet) is .
Then, the surface area of the circular base would be
square feet.
The volume of a cone with base area and height is ,
so for our cone, the volume (in cubic feet) is indeed
.

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