Question

A cylinder has a height of 15 inches. Its volume is 3,014.4 cubic inches. What is the radius of the cylinder?

Use ​ ≈ 3.14 and round your answer to the nearest hundredth.

Answer 1

To solve this problem where we need to find the radius:

⇒ find the relationship between height, volume, and radius

⇒ only equation that involves all these quantities is

⇒ Volume's equation =
`V = \pi r^2*h`

• V: volume ⇒ 3014.4 cubic inches
• r: length of radius
• h: length of height ⇒ 15 inches
• 
  `\pi` ≈ 3.14

Let's set up our volume equation with known quantities

`V=\pi r^2*h\\3014.4=\pi r^2*15\\3014.4 = 3.14*r^2*15\\960=15r^2\\r^2=64\\r=8`

*r cannot be negative thus r equals a positive 8

Thus the radius is 8.00 inches (rounded to the nearest hundredth)

Hope that helps!

Answer 2

8.00 inches

Explanation:

Given:

• height = 15 inches
• volume = 3,014.4 cubic inches

To find:

• radius

Cylinder’s Volume:

• 
  `\displaystyle \large{V=\pi r^2 h}`

Substitute given information in:

`\displaystyle \large{3,014.4 = 3.14 \cdot r^2 \cdot 15}\\\displaystyle \large{3,014.4=47.1r^2}`

Solve for r by dividing both sides by 47.1:

`\displaystyle \large{(3,014.4)/(47.1) = (47.1r^2)/(47.1)}\\\displaystyle \large{64 = r^2}\\\displaystyle \large{r = 8,-8}`

However, radius is a scalar value so it cannot be negative - the radius is 8 inches

Since you want in nearest hundredth then the radius is 8.00 inches