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.
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Calculate the radius of the sphere: \[ \text{Diameter} = 3 , \text{inches} \ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{3 , \text{inches}}{2} = 1.5 , \text{inches} \]
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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: \[ V \approx 14.155 , \text{cubic inches} \]
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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:
\[ \boxed{63.585 , \text{ounces}} \]
1 answer