Cubes and cuboids
Cubes and cuboids
Here are two aquariums filled with water. We are going to calculate how much water they can hold. In this problem we deal with the volume. Just like we can measure surfaces in meters squared or centimeters squared, we can also calculate volumes in units such as cubic meters and cubic centimeters. A cube with the side of one centimeter it's about as big as a sugar cube.
One way to measure an aquarium would be to fill it with cubes like this, and then count how many cubes you managed to fit in. But this wouldn't be practical and the answer wouldn't be precise. So we measure the aquarium instead. We'll start with this aquarium. The wider one.
Such a geometrical object where all the corners have right angles is called a rectangular prism. The bottom of this rectangular prism is a rectangular with the sides of 40 and 60 centimeters respectively, 40 times 60 centimeters is 24 hundred centimeters squared. We call a three dimensional object bottom a base. So far we have the area of the base, but to calculate the aquarium's volume we need to multiply all three dimensions, the height, the width, and the length. So we take the area of the base times the height.
The aquarium is 40 centimeters high, so we have 24 hundred square centimeters times 40 centimeters, 24 hundred times 40 is 96 thousand. And 1 centimeter squared times 1 centimeter is 1 cubic centimeter. Did you follow that? When measuring the area we take centimeter times centimeter, and we get centimeter squared. In the same way we get a new unit when calculating the volume.
Centimeter times centimeter times centimeter equals cubic centimeter. We write this as cm to the power of 3. Three because it's a three-dimensional object. And we can convert 96 thousand cubic centimeters to liters if we divide the number by a thousand, 96 liters of water if it's completely full. Shall we take a look at the other aquarium?
All the corners have right angles, and all the sides are equal. The length, the width, and height are 40 centimeters each. This aquarium is a cube. Here we can take a shortcut to calculate the volume. Instead of calculating the area of the base first and then multiplying the result by the height, you can do this directly on your calculator.
40 to the power of 3. This is 40 times itself 3 times. The answer is the same. But if you know what a cube is, and if you can work with powers, this is the fastest way to calculate the volume of a cube. Once more, here's what you need to remember. Volumes of a rectangular prism and a cube can always be calculated like this, x times y times z.
If a rectangular prism is a cube you can take a shortcut, since all three sides of a cube are equal. X to the power of 3. And when you calculate volumes, remember that the units are cubic centimeters if you measure in centimeters. Or cubic meters if you measure in meters.