Exercise 20 Page 758

We are given that Anna has cereal in a cylindrical container that has a diameter of 6 inches and a height of 12 inches. She wants to store the cereal in a rectangular prism container.

In our exercise we want to find one possible set of dimensions for the new container so that both containers would have close to the same volume. To do this we can use Cavalieri's Principle. Let's recall it.

This means that if the height of the rectangular prism is also 12 and the area of the base of this solid is equal to the area of a circle with a diameter of 6 inches, the containers will have the same volumes. Let a and b represent the dimensions of the base of the prism.

To find the possible values of a and b let's use the formulas for the area of a rectangle and the area of a circle. Remember that a radius of a circle is one half of the diameter. a b=π (6/2)^2 Let's simplify the equation.

ab=π(6/2)^2

▼

Simplify right-hand side

CalcQuot

Calculate quotient

ab=π(3)^2

CalcPow

Calculate power

ab=π(9)

UseCalc

Use a calculator

ab=28.2743...

RoundInt

Round to nearest integer

ab≈ 28

We found that the product of a and b needs to be equal to approximately 28. This is true, for example, for a= 4 and b= 7.

Therefore, one of the possible sets of dimensions for a rectangular prism container is 4in. * 7in.*12 inches.

Checking Our Answer

Evaluating the Volumes of the Containers

To check if our solution is correct, let's evaluate the volume of each container. To do this we will use the formulas for the volume of a cylinder and the volume of a rectangular prism.

Container	Formula	Simplify
Cylinder	π(6/2)^2 12	≈ 339
Rectangular Prism	( 4* 7)* 12	336

As we can see, the volume of the new container is close to the volume of the cylindrical container. Therefore, our solution is correct.