SOLUTION: The volume of a cone varies jointly as the height and the square of the radius of the base. A cone height 8 cm and a base of diameter 9 cm has volume 54π. Find the constant of
Algebra.Com
Question 196976This question is from textbook algebra and trigonometry
: The volume of a cone varies jointly as the height and the square of the radius of the base. A cone height 8 cm and a base of diameter 9 cm has volume 54π. Find the constant of variation and use it to develop the general formula for the volume of a cone.
This question is from textbook algebra and trigonometry
Found 2 solutions by solver91311, stanbon:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The volume varies jointly as the height and the square of the radius of the base means:
You are given that the volume is 
when the height is 8 and the diameter is 9. The diameter being 9 means that the radius is 4.5, so:
^2)
where 
is the constant of proportionality. Solve the above equation for and replace in the first equation with that value. (Hint: Leave it in terms of 
)
John
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The volume of a cone varies jointly as the height and the square of the radius of the base.
V = k[h*r^2]
------------------
A cone height 8 cm and a base of diameter 9 cm has volume 54π. Find the constant of variation and use it to develop the general formula for the volume of a cone.
54 = k[8*(9/2)^2]
54 = k[162]
k = 54/162
k = 1/3
---
Equation:
V = (1/3)h*r^2
===========================
Cheers,
Stan H.
-------------------------------
RELATED QUESTIONS
The volume of a cone varies jointly as its height and the square of the radius of its... (answered by ikleyn)
The volume of a cone varies jointly as its height and the square of the radius of its... (answered by Alan3354)
The volume of a cone varies jointly as its height and the square of its radius. A certain (answered by jorel1380)
3. The volume of a cone V varies jointly as it’s height h and the square of its radius r. (answered by Alan3354)
The volume of a cone varies jointly as its height, and the square of its radius.
If a... (answered by greenestamps)
3. The volume of a cone V varies jointly as it’s height h and the square of its radius r. (answered by josgarithmetic)
The volume of a cone varies jointly as the square of its radius and its height. If the... (answered by mukhopadhyay)
The volume of a cone varies jointly as the height and the square of the radius. Suppose a (answered by ikleyn,josgarithmetic)
A cone has a height of 5 cm and the area of base is 154 cm square. Find volume.
(answered by ikleyn)