Question

igure. round answers to the nearest hundredth, if necessary.
2)
12 mm
6 mm
volume:
3)
8 m
volume:
5)
14 in
6 in
volume:
6)
volume:
8)
12 in
8 in r
volume:
9)
volume:

Explanation:

Problem 2: Volume of Cone (6 mm diameter, 12 mm height)

Step1: Find the radius

The diameter is 6 mm, so radius \( r = \frac{6}{2} = 3 \) mm.

Step2: Use cone volume formula

The formula for the volume of a cone is \( V = \frac{1}{3}\pi r^2 h \). Substitute \( r = 3 \) mm and \( h = 12 \) mm.
\( V = \frac{1}{3} \times \pi \times 3^2 \times 12 \)

Step3: Calculate the volume

First, \( 3^2 = 9 \). Then, \( \frac{1}{3} \times 9 \times 12 = 3 \times 12 = 36 \). So \( V = 36\pi \approx 36 \times 3.1416 \approx 113.10 \) \( \text{mm}^3 \).

Step1: Identify values

Radius \( r = 6 \) in, height \( h = 14 \) in.

Step2: Apply cone volume formula

\( V = \frac{1}{3}\pi r^2 h \). Substitute \( r = 6 \) and \( h = 14 \).
\( V = \frac{1}{3} \times \pi \times 6^2 \times 14 \)

Step3: Compute the volume

\( 6^2 = 36 \). Then, \( \frac{1}{3} \times 36 \times 14 = 12 \times 14 = 168 \). So \( V = 168\pi \approx 168 \times 3.1416 \approx 527.79 \) \( \text{in}^3 \).

Step1: Recall cylinder volume formula

The formula for the volume of a cylinder is \( V = \pi r^2 h \).

Step2: Substitute values

Radius \( r = 8 \) in, height \( h = 12 \) in. So \( V = \pi \times 8^2 \times 12 \).

Step3: Calculate the volume

\( 8^2 = 64 \). Then, \( 64 \times 12 = 768 \). So \( V = 768\pi \approx 768 \times 3.1416 \approx 2412.74 \) \( \text{in}^3 \).

Answer:

\( 113.10 \text{ mm}^3 \) (or \( 36\pi \text{ mm}^3 \))

Problem 5: Volume of Cone (6 in radius, 14 in height)