Chapter 12.3, Problem 40HP

To determine

The given statement is true or false.

Answer to Problem 40HP

The given statement is false.

Explanation of Solution

Given data: $y$

Statement: A regular polygonal pyramid and a cone both have height h units and base perimeter P units. Therefore, they have the same total surface area.

Concept used:

The surface area of a cone ${\text{S}}_{\text{cone}}\text{=}\frac{P}{2}\sqrt{r^{\text{2}}\text{+}{h}^{\text{2}}}\text{+}B$ , and the surface area of the pyramid is given by ${\text{S}}_{\text{pyramid}}\text{=}\frac{P}{2}\sqrt{r^{\text{2}}\text{+}{h}^{\text{2}}}\text{+}B$ where P , h , r , and B arethe perimeter, height, radius of the base and the area of the base respectively.

When perimeter of the base of a cone and the pyramid are equal the inradius of the pyramid is equal to the radius of the base of the cone but area of the base of the pyramid not equal to the area of the base of pyramid. Given h , r , and P are equal but notB . Therefore, a cone and the pyramid never have equal surface area.

Hence, the given statement is false.

Conclusion:

The given statement is false.