Q70. - Algebra 2

Question

For Exercises 64-70, define a variable, write an equation, and solve the problem.

 

Two designs for a soup can are shown at the right. If each holds the same amount of soup, what is the height of can A?

Step-by-Step Solution

Answer

The required answer is $8.33$ approximately.

Step 1- Define the required variable

Consider h be the required height. 

Step 2 – Determine the storing capacity of Can B

Use the formula for volume of cylinder $V=\pi r^{2}h$ and substitute the provided radius and height of Can B into it.

 

$\begin{array}{c}V=\pi {\left(2\right)}^{2}3\\ =\frac{22}{7}\cdot 4\cdot 3\\ \approx 37.7\end{array}$

Step 3 – Form the equation

Take the variable h and form the equation by using the volume of cylinder $V=\pi r^{2}h$. Substitute the radius of can A and write the volume of can B in place of V into the formula.

$37.7=\pi {\left(1.2\right)}^{2}h$

Step 4- Solve the equation for h

Write the obtained equation in simplified form.

$37.7=\frac{22}{7}·1.44·h$

Perform division of $\frac{22}{7}$ and $1.44$ both sides of the equation.

$h\approx 8.33$

Step 5- Perform the checking

Substitute the obtained height and radius of Can A into the formula for volume of cylinder $V=\pi r^{2}h$.

$\begin{array}{c}V=\pi {\left(1.2\right)}^2\left(8.33\right)\\ \approx 37.7\end{array}$

This results in the volume of can B which means that the obtained answer is correct.