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bonufazy [111]
2 years ago
12

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 Ro

n'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.
Mathematics
1 answer:
Sphinxa [80]2 years ago
6 0

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.

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