Question

A cylinder with a 4-inch diameter and a 6-inch height holds 1 pound of oatmeal. To the nearest ounce, how much oatmeal will a similar 10-inch tall cylinder hold?

A) 37 Ounces
B) 44 Ounces
C) 74 Ounces
D) 192 Ounces

An explanation would be highly appreciated, I'm completely lost on this.

Answer 1

The answer is 74 ounces

Answer 2

Answer: Option 'c' is correct.

Explanation:

Since we have given that

Diameter of a cylinder = 4 inch

Radius of a cylinder = 2 inch

Height of this cylinder = 6 inch

So, volume of this cylinder is given by

`\pi r^2h\\\\=\pi * 2* 2* 6\\\\=24\pi cm^3`

If 24π cm³ holds 1 pound of oatmeal.

Then the similar cylinder with 10 inch tall cylinder will hold:

So, the radius of cylinder is given by

`(R1)/(R2)=(H1)/(H2)\\\\(2)/(x)=(6)/(10)\\\\x=(10)/(3)`

First we will calculate the volume of this cylinder is given by

`\pi r^2h\\\\=\pi* (10)/(3)* (10)/(3)* 10\\\\=(100)/(9)\pi cm^3`

As we know that

1 pound = 16 ounces

So, Amount of oatmeal
`(100)/(9)` π cm³ will hold:

`(16)/(24\pi)=(9y)/(100\pi)\\\\y=(2000)/(27)\\\\x=74.07\\\\x\approx 74`

Hence, Option 'c' is correct.