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

Step-by-step 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  $V=\frac{1}{3}a^2h$

$\therefore \text{height of Ron tower is}\ h_r=\dfrac{3V}{A_r}\\\\\Rightarrow h_r=\dfrac{3\times 320}{8}=120\ in.$

The height of Freddy tower is

$\Rightarrow h_f=\dfrac{3V}{A_f}\\\\\Rightarrow h_f=\dfrac{3\times 180}{6}=90\ in.$

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