Chapter 12.3, Problem 5CE

To determine

To find: Thevalues to complete the table.

Answer to Problem 5CE

The values are $l=5\text{units}$ , $L.A.=15\pi {\text{unit}}^2$ , $T.A=24\pi {\text{unit}}^2$ and $V=12\pi {\text{unit}}^3$ .

Explanation of Solution

Given information:

The given figure is shown below.

  

Figure (1)

Calculation:

The slant height of cone is.

  $l=\sqrt{r^2+h^2}$

Here, $l$ is the length of the circle, and $r$ is the radius, $h$ is the height.

The lateral area of cone is.

  $\pi rl$

The total area of cone is.

  $\pi rl+\pi r^2=\pi r\left(l+r\right)$

Volume of cone is.

  $\frac{1}{3}\pi r^{2}h$

The values are.

  $\begin{array}{l}r=3\\ h=4\end{array}$

The slant height of cone is.

  $\begin{array}{c}l=\sqrt{r^2+h^2}\\ =\sqrt{3^2+4^2}\\ =\sqrt{25}\\ =5\end{array}$

The lateral area of cone is.

  $\begin{array}{c}L.A.=\pi rl\\ =\pi \times 3\times 5\\ =15\pi {\text{unit}}^2\end{array}$

The total area of cone is.

  $\begin{array}{c}T.A=\pi rl+\pi r^2\\ =\pi r\left(l+r\right)\\ =\pi \times 3\left(8\right)\\ =24\pi {\text{unit}}^2\end{array}$

Volume of cone is.

  $\begin{array}{c}V=\frac{1}{3}\pi r^{2}h\\ =\frac{1}{3}\pi \times 3^2\times 4\\ =12\pi {\text{unit}}^3\end{array}$

Therefore, the values are $l=5\text{units}$ , $L.A.=15\pi {\text{unit}}^2$ , $T.A=24\pi {\text{unit}}^2$ and $V=12\pi {\text{unit}}^3$ .