Chapter 12.7, Problem 9PPS

To determine

To find: surface area of the silver bead.

Answer to Problem 9PPS

The surface area of the cone is $339.12{\text{mm}}^2$ andthe lateral area of the cone is approximately $275.535{\text{mm}}^2$

Explanation of Solution

Given:

  

Formula used:

The lateral area L of a cone is $L=\pi rl$ .

The surface area S of a cone is S = L + B.

Calculation:

The given figure is a cone.

The objective is to find the lateral and surface area of the cone.

Find the lateral area of the cone as shown below:

Since radius is half the diameter of a circle, so radius of the circle is $\frac{9}{2}$ mm that is

4.5 mm

Substitute r = 4.5 and l = 19.5 in the lateral area formula to find the lateral area of the cone.

Thus,

  $\begin{array}{c}L=\pi rl\\ =\pi \left(4.5\right)\left(19.5\right)\\ =87.75\pi \\ \approx 87.75\left(3.14\right)\left[Since\pi \approx 3.14\right]\\ =275.535\end{array}$

Therefore, the lateral area of the cone is approximately $275.535{\text{mm}}^2$

Find the surface area of the cone.

The area B of the cone is,

  $\begin{array}{c}B=\pi r^2\\ =\pi {\left(4.5\right)}^2\\ =20.25\pi \\ \approx 20.25\left(3.14\right)\left[Since\pi \approx 3.14\right]\\ =63.585\end{array}$

Substitute B = 63.585 and L = 275.535 in the surface area formula to find the surface area of the cone.

  $\begin{array}{c}S=L+B\\ \approx 275.535+63.585\\ =339.12\end{array}$

Conclusion:

Therefore, the surface area of the cone is $339.12{\text{mm}}^2$ andthe lateral area of the cone is approximately $275.535{\text{mm}}^2$