A design on the surface of a balloon is 5 cm wide when the balloon holds 71 cm^3 of air. How much air does the balloon hold when the design is 10 cm wide? Explain the method you use to find the amount of air.
To find the amount of air the balloon holds when the design is 10 cm wide, you can use the concept of similarity.
First, let's assume that the shape of the balloon when it holds 71 cm^3 of air is similar to the shape of the balloon when it holds the unknown amount of air with a 10 cm wide design.
Similar objects have corresponding sides in proportion to each other. This means that the ratio of corresponding sides will be equal.
Let's create a proportion using the width of the design on the balloon:
5 cm / 10 cm = (unknown air volume) / 71 cm^3
We can simplify the proportion to:
1/2 = (unknown air volume) / 71 cm^3
To solve for the unknown air volume, we can cross-multiply and solve the resulting equation:
2 * (unknown air volume) = 1 * 71 cm^3
Multiply 2 by 71 cm^3:
2 * (unknown air volume) = 71 cm^3
Divide both sides by 2 to solve for the unknown air volume:
(unknown air volume) = 71 cm^3 / 2
Calculate the result:
(unknown air volume) = 35.5 cm^3
Therefore, the balloon will hold approximately 35.5 cm^3 of air when the design is 10 cm wide.