Surface Area or Volume? What the Job Needs

0:00This water tank is a cylinder, with radius 0.5 metres and height 1.2 metres.

0:08Two jobs: how much water will it hold, and how much paint for its side and top?

0:14Water fills the space inside. That space is the volume, measured in cubic metres.

0:21Paint covers the outside. The total outside area is the surface area, measured in square metres.

0:28A cylinder's volume is its base area times its height: pi r squared h.

0:34Put in the numbers: pi times 0.5 squared times 1.2.

0:410.5 squared is 0.25, and 0.25 times 1.2 is 0.3. So the volume is 0.3 pi, about 0.942 cubic metres.

0:56A cubic metre is 1000 litres, so that is about 942 litres.

1:03Paint goes on the curved side and the top, not the bottom, which sits on the ground.

1:08Unrolled, the curved side is a rectangle, 2 pi r long, the distance around the circle, and 1.2 metres high.

1:17That is 2 times pi times 0.5 times 1.2, about 3.77 square metres.

1:25The top is a circle: pi times 0.5 squared, about 0.79 square metres.

1:33In total, 3.77 plus 0.79 is 4.56 square metres of paint.

1:41A common mistake is giving water in square metres. Water fills a space, so use cubic metres or litres.

1:50For a planter box, soil fills it, so that is volume. Paint covers its sides, so that is area.

1:58Rule of thumb: fill or hold means volume, in cubic metres. Cover or wrap means area, in square metres.