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.

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

$\pi r^2h\\\\=\pi \times 2\times 2\times 6\\\\=24\pi cm^3$

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

$\frac{R1}{R2}=\frac{H1}{H2}\\\\\frac{2}{x}=\frac{6}{10}\\\\x=\frac{10}{3}$

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

$\pi r^2h\\\\=\pi\times \frac{10}{3}\times \frac{10}{3}\times 10\\\\=\frac{100}{9}\pi cm^3$

As we know that

1 pound = 16 ounces

So, Amount of oatmeal $\frac{100}{9}$ π cm³ will hold:

$\frac{16}{24\pi}=\frac{9y}{100\pi}\\\\y=\frac{2000}{27}\\\\x=74.07\\\\x\approx 74$

Hence, Option 'c' is correct.