# Applying Volume and Surface Area

Warmup

Activity #1

Solve Application Problems.

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.

(1.) 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?

(2.) 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?

(3.) 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?

When he examines the play structure more closely, Kiran realizes it is really two separate pieces that are next to each other.

(1.) How does this affect the amount of foam in the play structure?

(2.) How does this affect the amount of vinyl covering the play structure?

Activity #2

Solve Application Problems.

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.

(1.) 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.)

(2.) 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?

(3.) 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?

(4.) 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?

Challenge #1

Shade in a base of the trapezoidal prism. (The base is not the same as the bottom.)

(1.) Find the area of the base you shaded.

(2.) Find the volume of this trapezoidal prism.

Challenge #2

A landscape architect is designing a pool that has this top view:

(1.) How much water will be needed to fill this pool 4 feet deep?

(2.) Before filling up the pool, it gets lined with a plastic liner. How much liner is needed for this pool?

Quiz Time