Question

find the volume of each cone. round the answer to two decimal places. (use π=3.14)
1)
volume =

2)
volume =

3)
volume =

Explanation:

1)

Step1: Recall the formula for the volume of a cone, which is \( V = \frac{1}{3}\pi r^2 h \), where \( r \) is the radius and \( h \) is the height. Here, \( r = 2.5 \, \text{cm} \) and \( h = 12.3 \, \text{cm} \), and \( \pi = 3.14 \).

Step2: Substitute the values into the formula. First, calculate \( r^2 \): \( (2.5)^2 = 6.25 \). Then, multiply by \( \pi \) and \( h \): \( 3.14 \times 6.25 \times 12.3 = 3.14 \times 76.875 = 241.3875 \). Finally, multiply by \( \frac{1}{3} \): \( \frac{1}{3} \times 241.3875 = 80.4625 \).

Step1: Use the cone volume formula \( V = \frac{1}{3}\pi r^2 h \). Here, \( r = 7.1 \, \text{ft} \) and \( h = 18.3 \, \text{ft} \), \( \pi = 3.14 \).

Step2: Calculate \( r^2 \): \( (7.1)^2 = 50.41 \). Then, \( 3.14 \times 50.41 \times 18.3 = 3.14 \times 922.503 = 2896.65942 \). Multiply by \( \frac{1}{3} \): \( \frac{1}{3} \times 2896.65942 \approx 965.55314 \).

Step1: The formula for the volume of a cone is \( V = \frac{1}{3}\pi r^2 h \). Here, the diameter is \( 5.8 \, \text{m} \), so the radius \( r = \frac{5.8}{2} = 2.9 \, \text{m} \), and \( h = 7.8 \, \text{m} \), \( \pi = 3.14 \).

Step2: Calculate \( r^2 \): \( (2.9)^2 = 8.41 \). Then, \( 3.14 \times 8.41 \times 7.8 = 3.14 \times 65.598 = 206.00 \) (approx). Multiply by \( \frac{1}{3} \): \( \frac{1}{3} \times 206.00 = 68.67 \) (approx, after rounding intermediate steps properly: \( 3.14\times8.41 = 26.4074 \), \( 26.4074\times7.8 = 205.97772 \), \( \frac{1}{3}\times205.97772 \approx 68.66 \)).

Answer:

\( 80.46 \, \text{cm}^3 \) (rounded to two decimal places)

2)