Chapter 10, Problem 26SGR

(a)

To determine

The formula $V=\pi r^{2}h$ for h .

Answer to Problem 26SGR

  $h=\frac{v}{\pi r^2}$

Explanation of Solution

Given information:

The equation: $V=\pi r^{2}h$ .

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve the formula for h, first divide each sides by pr², to simplify further as shown below:

  $\begin{array}{l}v=\pi r^{2}h\\ \frac{v}{\pi r^2}=\frac{\pi r^{2}h}{\pi r^2}\\ \frac{v}{\pi r^2}=h\\ h=\frac{v}{\pi r^2}\end{array}$

Thus, the formula is $h=\frac{v}{\pi r^2}$ .

(b)

To determine

To find the height of the container with volume 56.56 cubic inches and radius is 1.5 inches.

Answer to Problem 26SGR

  $h=8\text{inches}$

Explanation of Solution

Given:

  $h=\frac{v}{\pi r^2}$

  $\begin{array}{l}volume=56.52\\ radius=1.5\end{array}$

CALCULATION:

  $\begin{array}{l}h=\frac{v}{\pi r^2}\\ h=\frac{56.52}{3.14{\left(1.5\right)}^2}\\ h=8\end{array}$

Thus the height of the container is approximately

  $h=8\text{inches}$