Video: KS2-M17 • Paper 3 • Question 24

Cube 𝐴 and cuboid 𝐵 have the same volume. Calculate the missing length on cuboid 𝐵 in centimeters.

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Video Transcript

Cube 𝐴 and cuboid 𝐵 have the same volume. Calculate the missing length on cuboid 𝐵 in centimeters.

We’re told that the cube and the cuboid have the same volume. We can’t calculate the volume of cuboid 𝐵 because the length of one of the sides is missing. You may also be thinking we can’t calculate the volume of cube 𝐴 because only the length is given. But this is a cube which means all of its sides are equal in length. We calculate volume by multiplying the length times the width times the height. So we can calculate the volume of cube 𝐴 by multiplying six times six times six. We know that six times six is 36. Now we need to calculate 36 times six. 30 times six is 180 and six times six is 36. 180 plus 36 is 216. So we know the volume of cube 𝐴 is 216 centimeters cubed.

The volume of cuboid 𝐵 is also 216 centimeters cubed. We can use this information to help us find the missing length. We can use the inverse to help calculate the answer. Two of the sides are given, one is four centimeters and one is six centimeters. We could divide 216 by either of these sides to begin with. Let’s do 216 divided by four. There are no fours in two. So we need to divide 21 by four. Five fours are 20 which means we have a remainder of one. 16 divided by four is four. so 216 divided by four is 54. Now we can divide 54 by six. Six centimeters is the length of the other side that we’re given. 54 divided by six is nine. So the missing length is nine centimeters.

To find the answer, first, we calculated the volume of cube 𝐴. Once we had this volume, we were able to work backwards using the invoice. We divided 216 by the length of one side, which is four centimeters. Then we divided the answer by the length of the other side, which was six centimeters. This gave us the missing length, which was nine centimeters.