Question

to the nearest hundredth, if necessary.
3)
volume:
(image of a cylinder with radius 8 mm and height 12 mm)
6)
volume:
(image of a cylinder with radius 6 cm and height 8 cm)
9)
(image of a cylinder with height 6 ft and another with height 12 in)

Explanation:

Problem 3 (Cylinder with \( r = 8 \, \text{mm}, h = 12 \, \text{mm} \))

Step 1: Recall the formula for the volume of a cylinder.

The volume \( V \) of a cylinder is given by \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height.

Step 2: Substitute the given values into the formula.

Here, \( r = 8 \, \text{mm} \) and \( h = 12 \, \text{mm} \). So we have:
\( V = \pi \times (8)^2 \times 12 \)

Step 3: Calculate the value.

First, calculate \( 8^2 = 64 \). Then, multiply by 12: \( 64 \times 12 = 768 \). Now, multiply by \( \pi \): \( V = 768\pi \approx 768 \times 3.1416 \approx 2412.74 \, \text{cubic millimeters} \) (rounded to the nearest hundredth).

Step 1: Recall the formula for the volume of a cylinder.

The volume \( V \) of a cylinder is \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height.

Step 2: Substitute the given values into the formula.

Here, \( r = 6 \, \text{cm} \) and \( h = 8 \, \text{cm} \). So:
\( V = \pi \times (6)^2 \times 8 \)

Step 3: Calculate the value.

First, calculate \( 6^2 = 36 \). Then, multiply by 8: \( 36 \times 8 = 288 \). Now, multiply by \( \pi \): \( V = 288\pi \approx 288 \times 3.1416 \approx 904.78 \, \text{cubic centimeters} \) (rounded to the nearest hundredth).

Answer:

\( \approx 2412.74 \, \text{mm}^3 \)

Problem 6 (Cylinder with \( r = 6 \, \text{cm}, h = 8 \, \text{cm} \))