To determine which statement is true about the volumes of the blue and red exercise balls, we can calculate the volumes using the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.
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Calculate the radius of each ball:
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Blue ball: Diameter = 56 cm, so the radius \( r_b = \frac{56}{2} = 28 \) cm.
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Red ball: Diameter = 76 cm, so the radius \( r_r = \frac{76}{2} = 38 \) cm.
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Calculate the volume of each ball:
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Volume of the blue ball \( V_b \): \[ V_b = \frac{4}{3} \pi (28)^3 \] \[ V_b \approx \frac{4}{3} \pi \times 21952 \approx \frac{4}{3} \times 3.14 \times 21952 \approx 91634.67 \text{ cm}^3 \]
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Volume of the red ball \( V_r \): \[ V_r = \frac{4}{3} \pi (38)^3 \] \[ V_r \approx \frac{4}{3} \pi \times 54872 \approx \frac{4}{3} \times 3.14 \times 54872 \approx 229526.79 \text{ cm}^3 \]
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Compare the volumes:
Now we need to determine how many times larger the volume of the red ball is compared to the volume of the blue ball: \[ \text{Ratio} = \frac{V_r}{V_b} \approx \frac{229526.79}{91634.67} \approx 2.5 \]
From this calculation, we find that the volume of the red ball is about 2.5 times larger than the volume of the blue ball.
Therefore, the correct statement is:
The volume of the red ball is about 2.5 times larger than the volume of the blue ball.