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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.

User Aniztar
by
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2 Answers

2 votes

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!

User Ajay Kelkar
by
7.4k points
3 votes

Answer:

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

User JinSnow
by
8.5k points
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