When fully inflated, a blue exercise ball has a diameter of 56 cm. A similar red exercise ball, when fully inflated, has a diameter of 76 cm. Which statement is true?(1 point)
Responses
The volume of the red ball is about 1.5 times larger than the volume of the blue ball.
The volume of the red ball is about 1.5 times larger than the volume of the blue ball.
The volume of the blue ball is about 2.5 times larger than the volume of the red ball.
The volume of the blue ball is about 2.5 times larger than the volume of the red ball.
The volume of the blue ball is about 1.5 times larger than the volume of the red ball.
The volume of the blue ball is about 1.5 times larger than the volume of the red ball.
The volume of the red ball is about 2.5 times larger than the volume of the blue ball.
The volume of the red ball is about 2.5 times larger than the volume of the blue ball.
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The volume of the red ball is about 2.5 times larger than the volume of the blue ball.
Explanation:
The volume of a sphere is calculated using the formula V = 4/3 * π * r^3, where r is the radius of the sphere.
The radius of the blue exercise ball is half of the diameter, so it is 28 cm. The volume of the blue ball is therefore V_blue = 4/3 * π * 28^3 ≈ 71871.77 cm^3.
Similarly, the radius of the red exercise ball is half of the diameter, so it is 38 cm. The volume of the red ball is therefore V_red = 4/3 * π * 38^3 ≈ 92085.64 cm^3.
Comparing the volumes, we have V_red/V_blue ≈ 92085.64/71871.77 ≈ 1.28.
Therefore, the volume of the red ball is about 1.28 times larger than the volume of the blue ball.