Chapter 12.8, Problem 2P

To determine

To calculate: The height if the lateral surface area is $588c{m}^2$ and the diameter is $7.8cm$ , for a diameter of $10.4cm$ and height $18cm$ the lateral surface area is $588c{m}^2$ .

Answer to Problem 2P

The volume is $104c{m}^3$ .

Explanation of Solution

Given information:

The height if the lateral surface area is $588c{m}^2$ and the diameter is $7.8cm$ , for a diameter of $10.4cm$ and height $18cm$ the lateral surface area is $588c{m}^2$ .

The lateral surface area of a cylindrical jar varies jointly as the diameter and the height of the jar.

Formula used:

When area is given and height or diameter is to be find then:

  $2\Pi rh=$ given area

For varies jointly:

  $\frac{A_1}{D_1{H}_1}=\frac{A_2}{D_2{H}_2}$

Calculation:

Consider, The height if the lateral surface area is $588c{m}^2$ and the diameter is $7.8cm$ , for a diameter of $10.4cm$ and height $18cm$ the lateral surface area is $588c{m}^2$ .

The lateral surface area of a cylindrical jar varies jointly as the diameter and the height of the jar.

Recall that the lateral surface area of a cylinder for finding height in case area is given:

  $2\Pi rh=$ given area

For varies jointly:

  $\frac{A_1}{D_1{H}_1}=\frac{A_2}{D_2{H}_2}$

Therefore, volume of pyramid is given by,

  $\begin{array}{c}\frac{588}{10.4\times 18}=\frac{294}{7.8\times H_2}\\ 588\times 7.8\times H_2=294\times 0.4\times 18\\ H_2=\frac{294\times 0.4\times 18}{588\times 7.8}\\ H_2=\frac{10.4\times 9}{7.8}\end{array}$

Then the height is:

  $\begin{array}{l}{H}_2=\frac{10.4\times 9}{7.8}\\ H_2=12cm\end{array}$

Thus, the height of a cylindrical jar is: $12cm$ .