Distinguishing Volume and Surface Area

Warmup

Use the unit square to find the area of the shape. Try as many problems as you can.

Activity #1

Differentiate Surface Area from Volume.

• The sliders below control the radius and height of the cylinder. ​
• Adjust the sliders to explore multiple cylinders. ​
• Examine the relationship between the area of the circular base and the volume of the cylinder.

Based on your observations, describe how to compute the VOLUME of any cylinder.

Activity #2

Distinguish Between Surface Area and Volume.

• Sort the cards into two groups based on whether it would make more sense to think about the surface area or the volume of the figure when answering the question.

Challenge #1

Select all the situations where knowing the volume of an object would be more useful than knowing its surface area.

Challenge #2

The depth of this heart-shaped box of chocolates is 2 inches.

How much cardboard is needed to create the box?

Challenge #3

A wheelbarrow is being used to carry wet concrete. Here are its dimensions.

(1.) What volume of concrete would it take to fill the tray?

(2.) After dumping the wet concrete, you notice that a thin film is left on the inside of the tray. What is the area of the concrete coating the tray? (Remember, there is no top.)

Quiz Time

https://www.ixl.com/math/geometry/surface-area-and-volume-of-rectangular-prisms