Question

A foam cylinder, with a diameter of 3 inches and height of 8 inches, is carved into the shape of a cone. What is the maximum volume of a cone that can be carved? Round your answer to the hundredths place.Group of answer choices75.40 in318.85 in328.27 in356.55 in3

Answer 1

Step 1:

In this question, we are given the following:

A foam cylinder, with a diameter of 3 inches and a height of 8 inches, is carved into the shape of a cone.

What is the maximum volume of a cone that can be carved? Round your answer to the hundredth place.

Step 2:

The details of the solution are as follows:

`\begin{gathered} Volume\text{ of a cylinder = }\pi\text{ r}^2h \\ where\text{ radius, r = }(Diameter)/(2)=\frac{3\text{ inches}}{2} \end{gathered}`
`Height,\text{ h = 8 inches}`
`Volume\text{ of the cylinder = }\pi\text{ x \lparen}(3)/(2))^2\text{ x 8 = 18 }\pi\text{ inches}^3`
`\begin{gathered} Then,\text{ volume of the cone = }(1)/(3)\pi r^2h\text{ = }(1)/(3)\text{ \lparen }\pi r^2h)\text{ = }(1)/(3)\text{ \lparen 18}\pi\text{ \rparen = 6 }\pi \\ Hence,\text{ the maximum volume of the cone = 18. 85 inches}^3\text{ \lparen OPTION B \rparen} \end{gathered}`

CONCLUSION:

The