vanillachips321
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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.

Respuesta :

linandrew41

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 = [tex]V = \pi r^2*h[/tex]

  • V: volume              ⇒ 3014.4 cubic inches
  • r: length of radius
  • h: length of height ⇒ 15 inches
  • [tex]\pi[/tex] ≈ 3.14

Let's set up our volume equation with known quantities

 [tex]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[/tex]

  *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!

VectorFundament120

Answer:

8.00 inches

Step-by-step explanation:

Given:

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

To find:

  • radius

Cylinder’s Volume:

  • [tex]\displaystyle \large{V=\pi r^2 h}[/tex]

Substitute given information in:

[tex]\displaystyle \large{3,014.4 = 3.14 \cdot r^2 \cdot 15}\\\displaystyle \large{3,014.4=47.1r^2}[/tex]

Solve for r by dividing both sides by 47.1:

[tex]\displaystyle \large{\dfrac{3,014.4}{47.1} = \dfrac{47.1r^2}{47.1}}\\\displaystyle \large{64 = r^2}\\\displaystyle \large{r = 8,-8}[/tex]

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

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