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
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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
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:
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 )
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]
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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
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Equation:
V = (1/3)h*r^2
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Cheers,
Stan H.
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