Question

Ron and Freddy built structures out of snap cubes. Ron's tower had an 8-inch square base. Freddy had a 6-inch square base. If Ron's tower had a volume of 320 cubic inches and Freddy's had a volume of 180 cubic inches, Whose tower was taller? Explain your reasoning.

Answer 1

Answer: Ron tower's

Explanation:

Given

Ron tower has a base of
`A_r=8\ in.^2`

Freddy tower has a base of
`A_f=6\ in.^2`

Suppose the tower is in the shape of a square prism

The volume of Ron and Freddy tower is
`320\ \text{and}\ 180\ in.^3`

The volume of a square-based prism is
`V=(1)/(3)a^2h`

`\therefore \text{height of Ron tower is}\ h_r=(3V)/(A_r)\\\\\Rightarrow h_r=(3* 320)/(8)=120\ in.`

The height of Freddy tower is

`\Rightarrow h_f=(3V)/(A_f)\\\\\Rightarrow h_f=(3* 180)/(6)=90\ in.`

Thus, the height of Ron's tower is more than Freddy's tower by
`30\ in.`