A container is an inverted cone with vertical axis, height and top radius . Water in it is deep and the water level is falling at . At what rate is the volume of water decreasing, in , to significant figures?
Answer and explanation
Correct answer: D. 6.28
- Step 1: By similar triangles, express water radius in terms of height : . Volume of water is .
- Step 2: Differentiate volume with respect to time using the chain rule: .
- Step 3: Substitute water depth and rate of falling : . The volume decreases at .
Answer
6.28.
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