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.Com
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
.
RELATED QUESTIONS
cylindrical tank. Willard is designing a cylindrical tank with cone-shaped ends. The... (answered by Theo)
A water tank in the shape of an inverted cone has height 11 feet and radius 5.0 feet.... (answered by solver91311)
The interior dimensions of a rectangular fish tank are 4 feet long, 3 feet wide, and 2... (answered by checkley77)
A conical Oil storage tank is being designed. The tank must hold 271 cubic feet of Oil... (answered by Alan3354)
A cylinder tank can hold 2279.64 cubic feet of water. The diameter of the tank is 11... (answered by macston)
If a right circular cone has a volume of 15 cubic feet and a radius of 3 feet, what is... (answered by Fombitz)
THE VOLUME OF A CYLINDRICAL TANK IS GIVEN BY THE FORMULA V=pie h r^2 WHERE h IS THE... (answered by checkley75)
Problem-
A cylindrical storage tank has a radius of 15 feet and a height of 30 feet.
(answered by ewatrrr)
A cylindrical storage tank has a radius of 15 feet and a height of 30 feet. What is the... (answered by mananth)