Chapter 12.7, Problem 14PPS

To determine

To find: the lateral area of the cone

Answer to Problem 14PPS

The surface area of the cone is $1178.29{\text{cm}}^2$ andthe lateral area of the cone is $894.9{\text{cm}}^2$

Explanation of Solution

Given:

Diameter 19 cm, slant height 30 cm

Calculation:

Since radius is half the diameter of a circle.

Therefore, radius of the circle is.

  $\begin{array}{c}r=\frac{19}{2}\text{cm}\\ \text{=9}\text{.5}\text{cm}\end{array}$

  $\text{9}\text{.5}\text{cm}$

Substitute r = 9.5 and l = 30 in $L=\pi rl$

Thus,

  $\begin{array}{c}L=\pi rl\\ =\pi \left(9.5\right)\left(30\right)\\ =285\pi \\ \approx 285\left(3.14\right)As\pi \approx 3.14\\ =894.9\end{array}$

Hence, the lateral area of the cone is approximately $894.9{\text{cm}}^2$

Find the surface area of the cone as follows:

The area B ofthe base is $B=\pi r^2$ .

  $\begin{array}{c}B=\pi r^2\\ =\pi {\left(9.5\right)}^2\\ =90.25\pi \\ \approx 90.25\left(3.14\right)\\ =283.385\end{array}$

Substitute B = 283.385 and L = 894.9 in S = L + B

  $\begin{array}{c}S=L+B\\ \approx 283.385+894.9\\ \approx 1178.29\end{array}$

Conclusion:

Hence, the surface area of the cone is $1178.29{\text{cm}}^2$ andthe lateral area of the cone is $894.9{\text{cm}}^2$