Video: KS2-M19 • Paper 2 • Question 23

Amina made this cuboid using centimetre cubes. Stefan makes a cuboid that is 5 cm longer, 5 cm taller, and 5 cm wider than Amina’s cuboid. What is the difference in the number of cubes in Amina’s and Stefan’s cuboids?

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Video Transcript

Amina made this cuboid using centimetre cubes. Stefan makes a cuboid that is five centimetres longer, five centimetres taller, and five centimetres wider than Amina’s cuboid. What is the difference in the number of cubes in Amina’s and Stefan’s cuboids?

This is a three-step problem. First, we have to find the volume of Amina’s cuboid. Then, we have to find the volume of Stefan’s cuboid. Then, we have to find the difference. We need to know how to calculate the volume first. We do this by multiplying the length by the width by the height. Amina’s cuboid is six by four by three. We know that six times four is 24. 24 multiplied by three is 72. So the volume of Amina’s cuboid is 72 centimetres cubed.

We know that Stefan’s cuboid is five centimetres longer, taller, and wider than Amina’s. Six centimetres plus five is 11, four plus five is nine, and three plus five is eight. To find the volume of Stefan’s cuboid, we need to multiply 11 by nine by eight. 11 times nine is 99. Now, we just need to multiply 99 by eight. An easy way to calculate this would be to round 99 to 100 and multiply 100 by eight, which is 800. Then, we need to adjust by taking away the eight ones that we added too many. Stefan’s cuboid is 792 centimetres cubed.

Now, all we need to do is find the difference. 792 take away 72 equals 720. The difference between Stefan and Amina’s cuboids is 720 cubes.

To solve this problem, first, we found the volume of Amina’s cuboid. Then, we found the volume of Stefan’s cuboid. And then, we found the difference.

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