Chapter 12.3, Problem 37WE

To determine

To calculate: The lateral area of the cone and the pyramid

Answer to Problem 37WE

The lateral area of the cone and pyramid is 129.69 sq. units and 171.54 sq. units

Explanation of Solution

Given information: Consider the given information,

A regular hexagonal pyramid is inscribed in a cone

Base edge = 6 units

Height = 8 units

  $\pi \approx 3.14$

Formula used: Consider the given formula,

r = radius, h = height, a=edge

Lateral area of cone = $\pi r\sqrt{h^2+r^2}$

Lateral area of pyramid = $3a\sqrt{h^2+{\frac{3a}{4}}^2}$

Calculation : Consider the given information the formula is,

Ratio of parallel sides of an isosceles trapezium ABCD =2:3

If AB = 6 then, CD = $6\times \frac{3}{2}=9$

Therefore, $2r=9$

  $r=\frac{9}{2}=4.5$ units

Lateral area of cone = $(3.14)\times (4.5)\sqrt{8^2+{4.5}^2}=129.69$ sq. units

Lateral area of pyramid = $3\times 6\sqrt{8^2+{\frac{3(6)}{4}}^2}$ = $18\sqrt{64+\frac{108}{4}}$

  $=18\sqrt{64+27}$

  $=18\times 9.53=171.54$ sq. units