Differential and Integral Calculus by Feliciano and Uy, Exercise 1.1, Problem 7

A right circular cylinder, radius of base x, height y, is inscribed in a right circular cone, radius of base r and a height h. Express y as a function of x (r and h are constants).

SOLUTION:

Refer to the figure below.

Differential and Integral Calculus by Feliciano and Uy, Exercise 1.1, Problem 7

By ratio and Proportion of two similar triangles, we have

\frac{y}{r-x}=\frac{h}{r}

y=\frac{h\left(r-x\right)\:}{r}

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