Chapter 10.6, Problem 20E

To determine

To calculate the lateral surface area of cone.

Answer to Problem 20E

  $7$ in²

Explanation of Solution

Given Information: Cone Diameter d = 1 in.,Height h= 2 in. and $\pi =\frac{22}{7}$

Formula Used:

Lateral Surface area of Cone = $\pi rl$ , Slant height $l=\sqrt{h^2+r^2}$ , Radius = $\frac{Diameter}{2}$

Calculation:

Diameter d = 2 in., Height h = 2 in. and $\pi =\frac{22}{7}$

First find Radius r.

Hence,

Radius = $\frac{Diameter}{2}$

Put the value of diameter to find radius of Cone

Radius = $\frac{2}{2}$

So,

Radius r = 1 in.

Now, find Slant Height l.

Slant Height of Cone $l=\sqrt{h^2+r^2}$

Radius r = 1 in, Height h = 2 in

Now put the value of r and h to find Slant Height of Cone

Slant Height of Cone $l=\sqrt{2^2+1^2}$ in

So,

Slant Height of Cone $l=\sqrt{4+1}$ in

Hence,

Slant Height of Cone $l=\sqrt{5}$ in

Lateral Surface area of Cone = $\pi rl$

Radius r = 1 in., Slant Height $l=\sqrt{5}$ in. and $\pi =\frac{22}{7}$

Now put the value of r, s and $\pi$ to find Lateral Surface area of Cone

Lateral Surface area of Cone = $\frac{22}{7}\times 1\times \sqrt{5}$ in²

Hence,

Lateral Surface area of Cone = $7.027$ in²

Nearest Lateral Surface area of Cone = $7$ in²