Section 1
Real-World Applications
Property
Real-world objects often require both volume and surface area calculations. Always read carefully to decide which one you need:
- Filling an object (water, dirt, air) = Volume.
- Covering an object (paint, wrapping paper, tile) = Surface Area.
Examples
- Swimming Pool (Volume): An L-shaped pool has a shallow end (10 ft by 12 ft, depth 4 ft) and a deep end (15 ft by 12 ft, depth 9 ft).
Volume of shallow end: 10 x 12 x 4 = 480 cubic ft.
Volume of deep end: 15 x 12 x 9 = 1620 cubic ft.
Total water needed: 480 + 1620 = 2100 cubic ft.
- Skate Park Ramp (Surface Area): A wooden ramp is built from a rectangular prism and a triangular prism. To figure out how much special grip paint to buy, you must find the Surface Area. Remember to exclude the bottom faces touching the ground and the faces where the two prisms connect!
Explanation
Out in the real world, nobody hands you a perfectly simple cube! Pools, couches, houses, and skate ramps are all composite figures. By breaking these complex shapes into easy rectangular and triangular prisms, you can calculate exactly how much water fills a pool or how much paint covers a building. Just take it one block at a time!