Question

keep going! calculate the volume of each cone. use 3.14 for π. remember that the diameter of a circle is twice its radius. round your answer to the nearest hundredth if needed.

Explanation:

First Cone (in mm)

Step1: Find the radius

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

Step2: Use the cone volume formula \( V = \frac{1}{3}\pi r^2 h \)

Here, \( \pi = 3.14 \), \( r = 3 \) mm, \( h = 9 \) mm.
Substitute the values: \( V = \frac{1}{3} \times 3.14 \times 3^2 \times 9 \)
First, calculate \( 3^2 = 9 \). Then, \( \frac{1}{3} \times 3.14 \times 9 \times 9 \). \( \frac{1}{3} \times 9 = 3 \), so \( 3.14 \times 9 \times 3 = 3.14 \times 27 = 84.78 \) cubic millimeters.

Second Cone (in inches)

Step1: Identify radius and height

The diameter of the base is 12 in, so radius \( r = \frac{12}{2} = 6 \) in, and height \( h = 5 \) in.

Step2: Use the cone volume formula \( V = \frac{1}{3}\pi r^2 h \)

Substitute \( \pi = 3.14 \), \( r = 6 \) in, \( h = 5 \) in.
\( V = \frac{1}{3} \times 3.14 \times 6^2 \times 5 \)
Calculate \( 6^2 = 36 \). Then, \( \frac{1}{3} \times 3.14 \times 36 \times 5 \). \( \frac{1}{3} \times 36 = 12 \), so \( 3.14 \times 12 \times 5 = 3.14 \times 60 = 188.4 \) cubic inches.

Answer:

First cone (mm): \( 84.78 \) cubic millimeters
Second cone (in): \( 188.4 \) cubic inches