Question

A certain ball bearing is made of a grade of steel with a density of 4.5 ounces per cubic inch. The ball bearing is a solid sphere with a diameter of 3 inches.

What is the total weight of the ball bearing, in ounces? Use 3.14 for
.
63.585 ounces
127.17 ounces
190.755 ounces
508.68 ounces

Answer 1

To calculate the total weight of the ball bearing, we first need to find its volume and then use the density to find the weight.

1. **Calculate the radius of the sphere**:
\[
\text{Diameter} = 3 \, \text{inches} \\
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{3 \, \text{inches}}{2} = 1.5 \, \text{inches}
\]

2. **Calculate the volume of the sphere** using the formula for the volume of a sphere:
\[
V = \frac{4}{3} \pi r^3
\]
Plugging in the radius:
\[
V = \frac{4}{3} \times 3.14 \times (1.5)^3
\]

First, calculate \( (1.5)^3 \):
\[
(1.5)^3 = 1.5 \times 1.5 \times 1.5 = 3.375
\]

Now substitute back into the volume formula:
\[
V = \frac{4}{3} \times 3.14 \times 3.375 = \frac{4 \times 3.14 \times 3.375}{3}
\]
Calculate \( 4 \times 3.14 \):
\[
4 \times 3.14 = 12.56
\]
Now multiply by \( 3.375 \):
\[
12.56 \times 3.375 = 42.465
\]
Now divide by 3:
\[
V = \frac{42.465}{3} \approx 14.155
\]
So the volume of the sphere is approximately:
\[
V \approx 14.155 \, \text{cubic inches}
\]

3. **Calculate the weight of the ball bearing**:
Using the density (density = 4.5 ounces per cubic inch):
\[
\text{Weight} = \text{Density} \times \text{Volume}
\]
\[
\text{Weight} = 4.5 \, \text{oz/in}^3 \times 14.155 \, \text{in}^3
\]
Now, calculate the weight:
\[
\text{Weight} \approx 4.5 \times 14.155 \approx 63.6975 \, \text{ounces}
\]

Therefore, the total weight of the ball bearing is approximately **63.7 ounces**.

Among the options provided, the closest match is **63.585 ounces**. Thus, the answer is:

\[
\boxed{63.585 \, \text{ounces}}
\]