Question

The cone-shaped game piece is made of a metal with a density of 9.2 g/cm3. What is the mass of the game piece?

A tilted cone with diameter 3 centimeters, perpendicular height 4 centimeters, and slant height 5 centimeters.
A. 86.7 g
B. 92.6 g
C. 108.4 g
D. 231.2 g

Answer 1

To find the mass of the cone-shaped game piece, we first need to calculate the volume of the cone and then use the density to find the mass.

The formula for the volume \( V \) of a cone is given by:

\[
V = \frac{1}{3} \pi r^2 h
\]

where:
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone.

Given:
- Diameter of the cone = 3 cm (therefore, radius \( r = \frac{3}{2} = 1.5 \) cm)
- Height \( h = 4 \) cm

Now, we can substitute these values into the volume formula:

\[
V = \frac{1}{3} \pi (1.5)^2 (4)
\]

Calculating \( (1.5)^2 \):

\[
(1.5)^2 = 2.25
\]

Now substitute back into the volume equation:

\[
V = \frac{1}{3} \pi (2.25)(4)
\]

Calculating \( 2.25 \times 4 \):

\[
2.25 \times 4 = 9
\]

So now we have:

\[
V = \frac{1}{3} \pi (9)
\]
\[
V = 3 \pi \quad \text{(cubic centimeters)}
\]

Next, we can approximate \( \pi \) as \( 3.14 \):

\[
V \approx 3 \times 3.14 = 9.42 \text{ cm}^3
\]

Now, we will calculate the mass using the density formula:

\[
\text{mass} = \text{density} \times \text{volume}
\]

The density is given as \( 9.2 \, \text{g/cm}^3 \):

\[
\text{mass} = 9.2 \, \text{g/cm}^3 \times 9.42 \, \text{cm}^3
\]

Calculating that:

\[
\text{mass} \approx 9.2 \times 9.42 \approx 86.6 \, \text{g}
\]

Therefore, rounding to one decimal place:

\[
\text{mass} \approx 86.7 \, \text{g}
\]

The correct answer is:

**A. 86.7 g**