Chapter 10.6, Problem 23E

To determine

To calculate the surface area of cone.

Answer to Problem 23E

  $72$ yd²

Explanation of Solution

Given Information: Cone Diameter d = 5.8 yd., Height h = 4.1 yd. and $\pi =\frac{22}{7}$

Formula Used:

Surface area of Cone = $\pi r^2+\pi rl$

Calculation:

Surface area of Cone = $\pi r^2+\pi rl$

Diameter d = 5.8 yd., Height h = 4.1 yd. 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 = $\frac{5.8}{2}$

So,

Radius r = 2.9 yd.

Now, find Slant Height l.

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

Radius r = 2.9 yd., Height h = 4.1 yd.

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

Slant Height of Cone $l=\sqrt{{\left(4.1\right)}^2+{\left(2.9\right)}^2}$ yd.

So,

Slant Height of Cone $l=\sqrt{16.81+8.41}$ yd.

So,

Slant Height of Cone $l=\sqrt{25.22}$ yd.

Hence,

Slant Height of Cone $l=5.02$ yd.

Surface area of Cone = $\pi r^2+\pi rl$

Radius r = 2.9 yd., Slant Height l = 5.02 yd. and $\pi =\frac{22}{7}$

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

Surface area of Cone = $\frac{22}{7}\times {\left(2.9\right)}^2+\frac{22}{7}\times 2.9\times 5.02$ yd²

So,

Surface area of Cone = $\frac{22}{7}\times 2.9\times (2.9+5.02)$ yd²

So,

Surface area of Cone = $\frac{22}{7}\times 2.9\times 7.92$ yd²

Hence,

Surface area of Cone = $72.18$ yd²

Nearest Surface area of Cone = $72$ yd²