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? (2 points) Responses 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 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 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. The volume of the blue ball is about 2.5 times larger than the volume of the red ball.

Question

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? (2 points) Responses 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 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 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. The volume of the blue ball is about 2.5 times larger than the volume of the red ball.

Answer 1

The volume of the red ball is about 2.5 times larger than the volume of the blue ball.

To determine the volumes of the two balls, we use the formula for the volume of a sphere: V = (4/3)πr^3.

For the blue ball with a diameter of 56 cm, the radius is 28 cm. So, the volume of the blue ball is V_blue = (4/3)π(28)^3 ≈ 71999.56 cm^3.

For the red ball with a diameter of 76 cm, the radius is 38 cm. So, the volume of the red ball is V_red = (4/3)π(38)^3 ≈ 92041.48 cm^3.

Therefore, the volume of the red ball is about 1.5 times larger than the volume of the blue ball, making the statement "The volume of the red ball is about 2.5 times larger than the volume of the blue ball" true.