Math Problem Statement

If the water is dripping out from a conical vessel of semi- vertical angle π/4 at a uniform rate of 2 cm³/s through a tiny hole at the vertex in the bottom. When the slant height of the water is 4 cm, find the rate of-

(a) decrease of the water level.

(b) decrease of the slant height.

(c) decrease of the water surface area.

(d) decrease of the wetted surface of the vessel.

Solution

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Math Problem Analysis

Mathematical Concepts

Geometry
Calculus

Formulas

Volume of a cone
Related rates in calculus

Theorems

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Suitable Grade Level

Advanced High School