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.

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 ((D)/(2)) ^2(9)`

⇒
`\pi ((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.