The correct volume of the blue exercise ball is V_blue = 4/3 * π * (28/2)^3 = 4/3 * π * 14^3 = 14366.24 cm^3.
The correct volume of the red exercise ball is V_red = 4/3 * π * (38/2)^3 = 4/3 * π * 19^3 = 17924.11 cm^3.
Therefore, the correct comparison of volumes is V_red/V_blue ≈ 17924.11/14366.24 ≈ 1.25.
So the volume of the red exercise ball is approximately 1.25 times the volume of the blue exercise ball.
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.
these calculations are wrong
5 answers
ok this is the whole 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 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 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.
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 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 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.
To determine the correct statement, we can calculate the volumes of the blue and red exercise balls using the formula V = 4/3 * π * r^3, where r is the radius of the sphere.
For the blue exercise ball:
Radius = 56/2 = 28 cm
Volume = 4/3 * π * 28^3 ≈ 14366.24 cm^3
For the red exercise ball:
Radius = 76/2 = 38 cm
Volume = 4/3 * π * 38^3 ≈ 45738.91 cm^3
To compare the volumes:
V_red / V_blue ≈ 45738.91 / 14366.24 ≈ 3.19
Therefore, the correct statement is: The volume of the red ball is about 3.19 times larger than the volume of the blue ball.
For the blue exercise ball:
Radius = 56/2 = 28 cm
Volume = 4/3 * π * 28^3 ≈ 14366.24 cm^3
For the red exercise ball:
Radius = 76/2 = 38 cm
Volume = 4/3 * π * 38^3 ≈ 45738.91 cm^3
To compare the volumes:
V_red / V_blue ≈ 45738.91 / 14366.24 ≈ 3.19
Therefore, the correct statement is: The volume of the red ball is about 3.19 times larger than the volume of the blue ball.
those calculations still wrong.
4/3*3.14* 28^3 is 91905.71
4/3*3.14*38^3 is 229730.77
4/3*3.14* 28^3 is 91905.71
4/3*3.14*38^3 is 229730.77
Apologies for the error in the calculations. Let's correct the comparison of the volumes:
For the blue exercise ball:
Volume = 4/3 * π * 28^3 = 4/3 * 3.14 * 21952 ≈ 91905.71 cm^3
For the red exercise ball:
Volume = 4/3 * π * 38^3 = 4/3 * 3.14 * 54872 ≈ 229730.77 cm^3
To compare the volumes:
V_red / V_blue ≈ 229730.77 / 91905.71 ≈ 2.50
Therefore, the correct statement is: The volume of the red ball is about 2.5 times larger than the volume of the blue ball.
For the blue exercise ball:
Volume = 4/3 * π * 28^3 = 4/3 * 3.14 * 21952 ≈ 91905.71 cm^3
For the red exercise ball:
Volume = 4/3 * π * 38^3 = 4/3 * 3.14 * 54872 ≈ 229730.77 cm^3
To compare the volumes:
V_red / V_blue ≈ 229730.77 / 91905.71 ≈ 2.50
Therefore, the correct statement is: The volume of the red ball is about 2.5 times larger than the volume of the blue ball.