Video Transcript
A man needs to store 16,170 cubic
centimeters of rice in a container. He has one box which is a cuboid
with dimensions of 35 centimeters, 22 centimeters, and 21 centimeters and another
box which is a cube with length 22 centimeters. Which box should he use?
Remember a measure of capacity or
the amount of space a three-dimensional shape holds is volume. And the formula for the volume of a
rectangular prism or a cuboid is width times height times length. Essentially, it’s the product of
its three dimensions. Now, we can calculate this product
in any order. We also have a cube in this
question, but a cube is simply a cuboid whose dimensions are all equal. And so, the volume of a cube is
simply the length of one of its edges cubed. So, we’ll begin by calculating the
volume of each shape.
The dimensions of the cuboid are 35
centimeters, 22 centimeters, and 21 centimeters. So, the volume is 35 times 22 times
21, which is 16,170. Now, we’re multiplying centimeters
by centimeters by centimeters. And so, the units here are cubic
centimeters or centimeters cubed. Now, in fact, this is the exact
same value as the amount of rice that the man needs to store. But let’s double-check with the
volume of the cube.
This time, the length of each edge
is 22 centimeters. And so, the volume of our cube is
22 times 22 times 22 or 22 cubed. That gives us a volume of 10,648
cubic centimeters. This is indeed going to be too
small, so he should use the cuboid to store the rice.
