~ 7.16 ~
Applying Volume and Surface Area
Learning Targets
I can solve problems involving the volume and surface area of children’s play structures.
Notes
Suppose we wanted to make a concrete bench like the one shown in this picture. If we know that the finished bench has a volume of 10 ft3 and a surface area of 44 ft2 we can use this information to solve problems about the bench.
For example,
How much does the bench weigh?
How long does it take to wipe the whole bench clean?
How much will the materials cost to build the bench and to paint it?
To figure out how much the bench weighs, we can use its volume, 10 ft3. Concrete weighs about 150 pounds per cubic foot, so this bench weighs about 1,500 pounds, because 10 •150 = 1,500.
To figure out how long it takes to wipe the bench clean, we can use its surface area, 44 ft2. If it takes a person about 2 seconds per square foot to wipe a surface clean, then it would take about 88 seconds to clean this bench, because 44 • 2 = 88. It may take a little less than 88 seconds, since the surfaces where the bench is touching the ground do not need to be wiped.
Would you use the volume or the surface area of the bench to calculate the cost of the concrete needed to build this bench? And for the cost of the paint?
Activities
16.2 Foam Play Structure
Foam
Vinyl
At a daycare, Kiran sees children climbing on this foam play structure.
Kiran is thinking about building a structure like this for his younger cousins to play on.
The entire structure is made out of soft foam so the children don’t hurt themselves. How much foam would Kiran need to build this play structure? (Volume)
The entire structure is covered with vinyl so it is easy to wipe clean. How much vinyl would Kiran need to build this play structure? (Surface Area)
The foam costs 0.8¢ per in3. Here is a table that lists the costs for different amounts of vinyl. What is the total cost for all the foam and vinyl needed to build this play structure?
Angled View
Side View
16.3 Filling the Sandbox
The daycare has two sandboxes that are both prisms with regular hexagons as their bases. The smaller sandbox has a base area of 1,146 in2 and is filled 10 inches deep with sand.
It took 14 bags of sand to fill the small sandbox to this depth. What volume of sand comes in one bag? (Round to the nearest whole cubic inch.)
The daycare manager wants to add 3 more inches to the depth of the sand in the small sandbox. How many bags of sand will they need to buy?
The daycare manager also wants to add 3 more inches to the depth of the sand in the large sandbox. The base of the large sandbox is a scaled copy of the base of the small sandbox, with a scale factor of 1.5. How many bags of sand will they need to buy for the large sandbox?
A lawn and garden store is selling 6 bags of sand for $19.50. How much will they spend to buy all the new sand for both sandboxes?
Add to Your Notes
How do we use volume and surface area to solve more complex real-world problems?
You may need to calculate volume or surface area to answer a bigger question like how much it would cost to build something.
What other skills did you have to use to solve the problems in this lesson?
ratios and proportional relationships
Many times in real-world problems calculating the volume or surface area is just a small piece of what is needed to be done. There are many other skill involved in solving more complex problems!
Assignment
Check Google Classroom!