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A right circular cylinder has a height of 6 1/4. and a diameter of 3 1/2 times it's height.
What is the volume of the cylinder?
Enter your answer as a decimal in the box, just the number no units.
Use 3.14 for πt. Round your answer to the nearest hundredth.
volume =
diameter
height
decimal point
thousands
tens
tenths
thousandths

Verified Answer :

GinnyAnswer

To find the volume of a right circular cylinder with the given parameters, we need to follow these steps:

1. Convert the height to a decimal:
\(\( 6 \frac{1}{4} = 6 + 0.25 = 6.25 \)\)

2. Calculate the diameter:
The diameter is 3.5 times the height.
\(\[ \text{Diameter} = 3.5 \times 6.25 = 21.875 \]\)

3. Determine the radius:
The radius is half of the diameter.
\(\[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{21.875}{2} = 10.9375 \]\)

4. Use the formula for the volume of a cylinder:
The volume \(\( V \)\) of a cylinder is given by \(\( V = \pi r^2 h \)\).
Substituting \(\( \pi = 3.14 \)\), \(\( r = 10.9375 \)\), and \(\( h = 6.25 \)\):
\(\[ V = 3.14 \times (10.9375^2) \times 6.25 \]\)

5. Calculate the radius squared:
\(\[ 10.9375^2 = 119.62890625 \]\)

6. Calculate the volume:
\(\[ V = 3.14 \times 119.62890625 \times 6.25 \]\)
\(\[ V = 3.14 \times 747.6806640625 \]\)
\(\[ V = 2347.6752867953125 \]\)

7. Round to the nearest hundredth:
\(\[ \text{Volume} \approx 2347.68 \]\)

Therefore, the volume of the cylinder is \(\( \boxed{2347.68} \)\).

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