## 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-in

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.

in progress 0

1. Answer: Option ‘c’ is correct.

Step-by-step 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

[tex]pi r^2h=pi times 2times 2times 6=24pi cm^3[/tex]

If 24u03c0 cmu00b3 holds 1 pound of oatmeal.

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

So, the radius of cylinder is given by

[tex]frac{R1}{R2}=frac{H1}{H2}frac{2}{x}=frac{6}{10}x=frac{10}{3}[/tex]

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

[tex]pi r^2h=pitimes frac{10}{3}times frac{10}{3}times 10=frac{100}{9}pi cm^3[/tex]

As we know that

1 pound = 16 ounces

So, Amount of oatmeal [tex]frac{100}{9}[/tex] u03c0 cmu00b3 will hold:

[tex]frac{16}{24pi}=frac{9y}{100pi}y=frac{2000}{27}x=74.07xapprox 74[/tex]

Hence, Option ‘c’ is correct.

2. The answer is 74 ounces