Chapter 12.10, Problem 24HP

To determine

To calculate: To determine whether the given square pyramid has greater surface area of the cone.

Answer to Problem 24HP

Pyramid.

Explanation of Solution

Given information:

The given information is, A square pyramid with base X and slant height L and a cone with diameter X and Slant height L is given.

Calculation:

  $\begin{array}{l}Radiusofbaseofcone=\frac{x}{2}.\\ \therefore surfaceareaofcone=\pi \times \frac{x}{2}(\frac{x}{2}+l)\\ Now,areaofeachfaceofPyramidbe\Delta .\\ UsingPythagorastheorem,heightofeachfaceis\\ h=\sqrt{l^2-\frac{x^2}{4}}\\ \therefore surfaceareaofpyramid=4\times \frac{1}{2}\times \sqrt{l^2-\frac{x^2}{4}}\times x+x^2\\ =x\sqrt{4l^2-x+x^2}\\ Hencepyramidhasgreatersurfacearea.\end{array}$