To find out how much lead Lena will need for 80 solid metal balls with a diameter of 6 inches, we need to calculate the volume of one ball and then multiply that by 80.
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Calculate the radius of the ball: The radius \( r \) is half the diameter. \[ r = \frac{6 \text{ inches}}{2} = 3 \text{ inches} \]
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Calculate the volume of one ball using the formula for the volume of a sphere: \[ V = \frac{4}{3} \pi r^3 \] Substitute \( \pi \) (use 3.14) and \( r = 3 \): \[ V = \frac{4}{3} \times 3.14 \times (3)^3 \] Calculate \( (3)^3 \): \[ (3)^3 = 27 \] Now substitute back into the volume formula: \[ V = \frac{4}{3} \times 3.14 \times 27 \] First calculate \( \frac{4}{3} \times 27 \): \[ \frac{4 \times 27}{3} = \frac{108}{3} = 36 \] Now multiply by \( 3.14 \): \[ V = 36 \times 3.14 = 113.04 \text{ cubic inches} \]
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Calculate the total volume for 80 balls: \[ \text{Total Volume} = 80 \times 113.04 \] \[ \text{Total Volume} = 9043.2 \text{ cubic inches} \]
Therefore, Lena will need 9043.2 cubic inches of lead to make 80 balls.
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