~ 7.15 ~
Distinguishing Volume and Surface Area
Learning Targets
I can decide whether I need to find the surface area or volume when solving a problem about a real-world situation.
Notes
Sometimes we need to find the volume of a prism, and sometimes we need to find the surface area.
Volume
Surface Area
Here are some examples of quantities related to volume:
How much water a container can hold
How much material it took to build a solid object
Volume is measured in cubic units, like in3 or m3.
Here are some examples of quantities related to surface area:
How much fabric is needed to cover a surface
How much of an object needs to be painted
Surface area is measured in square units, like in2 or m2.
Activities
15.1 The Science Fair
Mai’s science teacher told her that when there is more ice touching the water in a glass, the ice melts faster. She wants to test this statement so she designs her science fair project to determine if crushed ice or ice cubes will melt faster in a drink.
She begins with two cups of warm water. In one cup, she puts a cube of ice. In a second cup, she puts crushed ice with the same volume as the cube. What is your hypothesis? Will the ice cube or crushed ice melt faster, or will they melt at the same rate? Explain your reasoning.
15.2 Revisiting the Box of Chocolates
The other day, you calculated the volume of this heart-shaped box of chocolates.
The depth of the box is 2 inches. How much cardboard is needed to create the box? (Surface Area)
15.3 Sort: Surface Area or Volume
Decide if it would make more sense to calculate surface area or the volume for each item. Explain your reasoning.
How much wood is needed to make triangular shaped stacking blocks?
How long it would take to fill a rectangular swimming pool?
How long it would take to dig dirt out to form a rectangular foundation for a new building?
How many yards of fabric needed to sew a pillowcase?
How much glass is needed to build a greenhouse?
How long would it take to paint the outside of a barn?
How much cardboard is needed to make a cereal box?
How much wood is needed to build a birdhouse?
Add to Your Notes
When is it necessary to consider surface area in solving a problem?
When you are covering an object, when you want to know how much is exposed to the environment, etc.
When is it necessary to consider volume in solving a problem?
When you are filling up an object, when you need to know how much is already inside, etc.
If you cut an object in half, how does that affect the volume and surface area?
The volume remains unchanged.
The surface area will increase!
Assignment
Check Google Classroom!