Bot GPT 4-o mini To find the volume of a cone, you can use the formula:
\[ V = \frac{1}{3} \pi r^2 h \]
Where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height, and
- \( \pi \) is approximately 3.14.
Step 1: Find the radius.
The diameter of the cone is 20 cm, so the radius \( r \) is:
\[ r = \frac{diameter}{2} = \frac{20 \text{ cm}}{2} = 10 \text{ cm} \]
Step 2: Plug in the values into the volume formula.
Now, substitute \( r = 10 \) cm, \( h = 15 \) cm, and \( \pi = 3.14 \):
\[ V = \frac{1}{3} \times 3.14 \times (10)^2 \times 15 \]
Step 3: Calculate \( (10)^2 \).
\[ (10)^2 = 100 \]
Step 4: Now substitute back into the volume formula.
\[ V = \frac{1}{3} \times 3.14 \times 100 \times 15 \]
Step 5: Calculate \( 100 \times 15 \).
\[ 100 \times 15 = 1500 \]
Step 6: Calculate the volume.
\[ V = \frac{1}{3} \times 3.14 \times 1500 \]
Now calculate \( 3.14 \times 1500 \):
\[ 3.14 \times 1500 = 4710 \]
Now divide by 3:
\[ V = \frac{4710}{3} = 1570 \]
So, the volume of the cone is:
\[ V \approx 1570 \text{ cubic centimeters} \]
The correct response is:
1,570 cubic centimeters.
1 answer