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

Algebra ->  Expressions-with-variables -> 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       Log On


   

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) About Me  (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 %281%2F3%29+pir%5E2h
r is the radius and h is the height
The expression for volume is%28+1%2F3%29pi+%28x+-+7%29%5E2+%28x+-+3%29
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%5E2
so The area of base = pi+%28x-7%29%5E2
B. The slant height is +sqrt%28r%5E2%2Bh%5E2%29
slant height = +sqrt%28%28x-7%29%5E2%2B%28x-3%29%5E2%29
= +sqrt%28x%5E2-14x%2B49+%2Bx%5E2-6x%2B9%29
=sqrt%282x%5E2-20x%2B58%29

curved surface area = pi r l
= pi+%2A+%28x-7%29%2Asqrt%282x%5E2-20x%2B58%29

Volume of 3 tanks is three times




Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of the tank is given by
%281%2F3%29pi%28x+-+7%29%5E2+%28x+-+3%29+
If you multiply that expression times 3, you get
pi%28x+-+7%29%5E2+%28x+-+3%29 , 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%28C%29 .

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%2Aradius%5E2=pi%28x+-+7%29%5E2 square feet.
The volume of a cone with base area A and height h is %281%2F3%29Ah ,
so for our cone, the volume (in cubic feet) is indeed
%281%2F3%29pi%28x+-+7%29%5E2+%28x+-+3%29+ .