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Area and Volume
三
Volume of a cone
Find the volume of a cone with a height of 10 yd and a base diameter of 12 yd.
Use the value 3.14 for it, and do not do any rounding.
Be sure to include the correct unit in your answer.
110 yd
I
12 yd
0

Verified Answer :

GinnyAnswer

To find the volume of the cone with the given dimensions, we will use the formula for the volume of a cone:

\(\[ V = \frac{1}{3} \pi r^2 h \]\)

Step-by-step solution:

1. Identify the given dimensions:
- The height (\(\( h \)\)) of the cone is 10 yards.
- The diameter of the base is 12 yards.

2. Calculate the radius (\(\( r \)\)) of the base:
Since the diameter is 12 yards,
\(\[ r = \frac{\text{diameter}}{2} = \frac{12}{2} = 6 \, \text{yards} \]\)

3. Substitute the known values into the volume formula:
\(\[ \pi \approx 3.14 \]\)
\(\[ h = 10 \, \text{yards} \]\)
\(\[ r = 6 \, \text{yards} \]\)

Plug these values into the formula:
\(\[ V = \frac{1}{3} \times 3.14 \times (6)^2 \times 10 \]\)

4. Calculate the volume:
- First, calculate \(\( (6)^2 \)\):
\(\[ 6^2 = 36 \]\)

- Next, multiply by \(\( \pi \)\):
\(\[ 3.14 \times 36 = 113.04 \]\)

- Then, multiply by the height:
\(\[ 113.04 \times 10 = 1130.4 \]\)

- Finally, multiply by \(\( \frac{1}{3} \)\):
\(\[ V = \frac{1}{3} \times 1130.4 \]\)
\(\[ V = 376.8 \]\)

Therefore, the volume of the cone is \(\( 376.8 \)\) cubic yards.

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