Basil the bumbling magician has done it again. Instead of pulling a rabbit out of a hat he pulled out rather smelly, ill tempered warthog. For now, he is keeping " Princess" in a cage with a volume of 27 cubic meters. If the sides are in whole meters only and the width is 3 meters, what are possible dimensions for the length and height?
What a convoluted question!
The cube root of 27 is 3.
The cage could be 3 by 3 by 3.
It could be 3 by 1 by 9.
To find the possible dimensions for the length and height of the cage, given that the width is 3 meters and the volume is 27 cubic meters, we can use the formula for the volume of a rectangular prism:
Volume = length × width × height
Given that the width is 3 meters and the volume is 27 cubic meters, we can rearrange the formula as follows:
27 = length × 3 × height
Simplifying further:
length × height = 27 / 3
length × height = 9
Now we need to find the possible pairs of whole numbers (length, height) that satisfy this equation and have a product of 9. Here are the possible pairs:
(1, 9), (3, 3), (9, 1)
These are the three possible dimensions for the length and height of the cage, given that the width is 3 meters: (1 meter, 9 meters), (3 meters, 3 meters), and (9 meters, 1 meter).