Question

Eugene believes that a prism with a square base of 14 centimeters and a height of 9 centimeters will have the same volume as a cylinder with a diameter of 14 centimeters and a height of 9 centimeters. Is Eugene correct? Explain your reasoning.

Answer 1

area of cylinder & prism aren't same,  Eugene is not correct.

Step-by-step explanation:

We have , Eugene believes that a prism with a square base of 14 centimeters and a height of 9 centimeters will have the same volume as a cylinder with a diameter of 14 centimeters and a height of 9 centimeters.

Volume of cylinder = $\pi r^2h$

⇒ $\pi r^2h$

⇒ $\pi (\frac{D}{2}) ^2(9)$

⇒ $\pi (\frac{14}{2}) ^2(9) = \pi (7^2)(9)$

⇒ $1384.74cm^3$

Volume of prism = $B(h)$ , where B is area of base!

⇒ $(side)^2(h)$

⇒ $(14)^2(9)$

⇒ $1764cm^3$

Since, area of cylinder & prism aren't same,  Eugene is not correct.