Chapter 12.8, Problem 6P

To determine

To calculate: The radius of another cone that has a height of $27\text{cm}$ and a volume of $576\pi c{m}^3$ .

The volume of a cone varies jointly as its height and the square of its radius. A certain cone has a volume of $702\pi c{m}^3$ , height of $15$ cm, and a radius of $12$ cm.

Answer to Problem 6P

The radius of the cone is: $14.58$ .

Explanation of Solution

Given information:

The cost of running an appliances varies jointly as the number of watts used, the hours of operation,

A $6000$ watt convection oven operates for $10$ min for $15$ at a cost of $7.5$ per kilowatt-hour. To calculate the cost of cooking two meals if each meal take; $70$ min to cook?

Formula used:

For varies jointly:

  $C=KWhc$

Calculation:

The cost of running an appliances varies jointly as the number of watts used, the hours of operation,

A $6000$ watt convection oven operates for $10$ min for $15$ at a cost of $7.5$ per kilowatt-hour. To calculate the cost of cooking two meals if each meal take; $70$ min to cook?

Recall that for varies jointly:

  $\begin{array}{l}V\alpha h{r}^2\\ V=Kh{r}^2\end{array}$

The values are:

  $V=720\pi ,h=15,r=12$

Therefore, the value of $k$ is,

  $\begin{array}{c}720\pi =K\times 15\times {12}^2\\ K=\frac{720\pi }{15\times 144}\\ K=73.125\pi \end{array}$

Now to find the value of $r$ ,

  $V_2=K{h}_2{r}_2{}^2$

The values are:

  $V=576\pi ,K=73.125\pi ,h=27$

Hence, when:

  $\begin{array}{c}576\pi =73.125\pi \times 27\times r_2{}^2\\ \frac{576\pi }{73125}=r_2{}^2\\ 212.676=r_2{}^2\\ \sqrt{212.676}=r_2\end{array}$

So,

  $\begin{array}{c}\sqrt{212.676}=r_2\\ 14.58=r_2\end{array}$

Thus, the radius of the cone is: $14.58$ .