Concept explainers
24. Filling a Conical Tank Water is poured into a container in the shape of a right circular cone with radius 4 feet and height 16 feet. See the figure. Express the volume V of the water in the cone as a function of the height h of the water. [Hint: The volume V of a cone of radius r and height h is .]
To find: To express the Volume of water in a cone as a function of height .
Answer to Problem 24AYU
Solution:
Explanation of Solution
Given:
Water is poured into a right circular cone of radius 4 feet and height 16 feet.
Calculation:
To express the Volume of the cone as a function of :
Volume of a cone .
From the figure, based on the properties of similar triangles, the ratio of sides can be written as
Where, .
Therefore, .
Substituting, .
Hence, the volume of the cone is .
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