Under the rules of the United States Golf Association the volume of a golf ball cannot be less than 2.48 cubic inches.
A. calculate the radius of this golf ball.
B. Calculate the circumference of this golf ball
*Please help i don't know how to do this!!*
(4/3)πr^3 ≥ 2.48
r^3 ≥ .592056...
r ≥ .8397 inches
circumference of ball is the circumference of circle with radius .8397
= 2πr
= 5.276 inches
A. To calculate the radius of the golf ball, we can use the formula for the volume of a sphere:
Volume of a sphere = (4/3)π * radius^3
We know that the volume of the golf ball cannot be less than 2.48 cubic inches. So we can set up the equation as:
2.48 = (4/3)π * radius^3
To solve for the radius, we need to rearrange the equation and solve for the radius:
radius^3 = (2.48 * 3) / (4π)
radius^3 = 1.86 / π
radius = ∛(1.86 / π)
Using a calculator to perform the cube root, we get:
radius ≈ 0.742 inches
B. To calculate the circumference of the golf ball, we can use the formula for the circumference of a sphere:
Circumference of a sphere = 2π * radius
Plugging in the value of the radius we calculated above, we get:
Circumference = 2π * 0.742
Circumference ≈ 4.652 inches
Therefore, the radius of the golf ball is approximately 0.742 inches and the circumference is approximately 4.652 inches.
To solve both parts of the problem, we need to understand the formulas for the volume, radius, and circumference of a sphere.
The volume of a sphere is given by the formula:
V = (4/3) * π * r^3
The radius of a sphere can be found by rearranging the volume formula:
r = (3V / (4π))^(1/3)
The circumference of a sphere is given by the formula:
C = 2 * π * r
Now, let's solve the problems step by step:
A. Calculate the radius of the golf ball:
Given that the volume of the golf ball cannot be less than 2.48 cubic inches, we can use the volume formula to find the radius.
1. Substitute the volume value into the formula:
2.48 = (4/3) * π * r^3
2. Rearrange the formula to solve for the radius:
r^3 = (3 * 2.48) / (4 * π)
r^3 = 1.86 / π
r ≈ (1.86 / π)^(1/3)
3. Use a calculator to evaluate the approximate value of the radius.
B. Calculate the circumference of the golf ball:
Now that we know the radius of the golf ball, we can use the circumference formula to find its circumference.
1. Substitute the radius value into the formula:
C = 2 * π * r
2. Calculate the value using the approximate radius obtained earlier.