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Chapter 2: Q. 24 (page 121)

Water is poured into a container in the shape of a right circular cone with radius 4feet 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 V=13蟺谤2h.]

Short Answer

Expert verified

The volume V of the water in the cone as a function of the height h of the water is V=蟺丑348.

Step by step solution

01

Step 1. Use the property of similar triangles.

We have given two similar triangles which gives

rh=416rh=14r=h4

02

Step 2. Use the formula for the volume of a cone.

The volume V of a cone is V=13蟺谤2h.

So the volume of cone as a function of height h is,

V=13蟺(h4)2h =蟺丑33(16)=蟺丑348

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