Question

Clare sketches a rectangular prism with a height of 11 and a square base and labels the edges of the base 8. She asks Han what he thinks will happen to the volume of the rectangular prism if she triples 8. Han says the volume will be 9 times bigger. Is he right? Explain or show your reasoning​

Answer 1

yes

Explanation:

Volume of rectangular prism = area of base x height

If the base is square with edges of 8, then area of base = 8 x 8 = 64

Therefore, volume = 64 x 11 = 704 units³

If the edges of the base are tripled, then an edge = 8 x 3 = 24

Therefore, the area of the base = 24 x 24 = 576

So volume = 576 x 11 = 6336 units³

Divide new volume by initial volume = 6336 ÷ 704 = 9

So yes, Han is right as the new volume is 9 times bigger.