1. Lesson 8

1.5. Explore 5

Mathematics 20-2 M6 Lesson 8

Module 6: Proportional Reasoning

 

Did You Know?


Algarrobo, Chile claims to be home to the world’s largest swimming pool. The San Alfonso del Mar pool, which was constructed in 2006, is 1012 m long.

A common misconception is that volume and capacity are the same when, in fact, they are not. Volume is the amount of space that is occupied by an object. Capacity is the amount that a container holds. So the volume of a swimming pool is the amount of space the entire pool takes up (including the walls) while the capacity of a swimming pool is the amount of water it holds.

 

 

This is a photo of a house in a box.

Comstock/Thinkstock

Rajesh, Kunal, and Akuti’s new neighbors, the Jones family, are building an in-ground pool and hot tub in their backyard. Once the pool was dug, Mr. Jones decided that it just wasn’t big enough. He told the contractor to make the whole thing 25% larger.

 

This illustration shows a set of blueprints for a rectangular pool that has a length of 32 feet, a width of 16 feet, and a depth of 8 feet. A cylindrical hot tub is located at one end of the pool. The hot tub has a diameter of 10 feet and a depth of 48 inches.

 

Try This 3
 

Mr. Jones didn’t specify to the contractor what was to be 25% larger: the dimensions, the surface area, or the volume of the pool. Use the applet Scaling Up a Pool to determine the difference between increasing the dimensions of the pool by 25%, increasing the area of the pool by 25%, or increasing the volume of the pool by 25%.

 

 

This is a screenshot for Scaling Up a Pool.

 

water: Hemera Technologies/AbleStock.com/Thinkstock;

characters: iStockphoto/Thinkstock

 

Share 1

 

This is an illustration of a hot tub that has a diameter of 10 feet and a depth of 48 inches. The hot tub is shaped like a right cylinder.

Work with a partner to determine the new dimensions of the hot tub when the dimensions are increased by 25%, the area is increased by 25%, and the volume in increased by 25%. Assume that the hot tub is shaped like a right cylinder. Go back and look at Scaling Up a Pool if you are having trouble.