Gerald was asked to find the radius and diameter of a cylinder with a volume of 502.4 m3 and a height of 10 m. He was also told to use 3.14 for

π
. Which of the TWO statements is correct?

A.
radius = 4 m

B.
radius = 16 m

C.
diameter = 32 m

D.
diameter = 2 m

E.
diameter = 8 m

1 answer

To find the radius and diameter of the cylinder, we can use the formula for the volume of a cylinder:

\[ V = \pi r^2 h \]

Where:

  • \( V \) = volume of the cylinder
  • \( r \) = radius
  • \( h \) = height
  • \( \pi \) is approximated as 3.14.

Given:

  • \( V = 502.4 , \text{m}^3 \)
  • \( h = 10 , \text{m} \)

We can rearrange the volume formula to solve for the radius \( r \):

\[ r^2 = \frac{V}{\pi h} \]

Substituting the known values:

\[ r^2 = \frac{502.4}{3.14 \times 10} \] \[ r^2 = \frac{502.4}{31.4} \] \[ r^2 = 16 \]

Now, taking the square root of both sides:

\[ r = 4 , \text{m} \]

Now, we can find the diameter \( d \) using the formula:

\[ d = 2r \] \[ d = 2 \times 4 , \text{m} = 8 , \text{m} \]

Now we can examine the answer choices:

A. radius = 4 m ✅

B. radius = 16 m

C. diameter = 32 m

D. diameter = 2 m

E. diameter = 8 m ✅

The correct statements are:

  • A: radius = 4 m
  • E: diameter = 8 m

So the two correct statements are A and E.