volume of a basketball is 448.9 cubic inches. with the formula V=4/3(pie)radius(cubed) for the volume of the ball, find the radius of the basketball
(4/3) pi r^3 = 448.9
r^3 = 107.167
r= 107.167^(1/3)
r = 4.75 inches
Well, first we need to solve the equation for the radius. Let's start by simplifying it a bit.
V = (4/3)(πr³)
To find the radius, we can rearrange the equation as follows:
r = ((3V)/(4π))^(1/3)
Now, let's substitute the given volume of the basketball into the equation:
r = ((3 * 448.9) / (4 * π))^(1/3)
Calculating that out, we get:
r ≈ 4.192 inches
So, the radius of the basketball is approximately 4.192 inches. Remember, approximations in real life are just the way the ball bounces!
To find the radius of the basketball, we can rearrange the volume formula and solve for the radius.
Given:
Volume of the basketball (V) = 448.9 cubic inches
Formula for volume of a sphere: V = (4/3) * π * r^3
Step 1: Write down the formula for the volume of a sphere:
V = (4/3) * π * r^3
Step 2: Substitute the given volume into the formula:
448.9 = (4/3) * π * r^3
Step 3: Divide both sides of the equation by (4/3) * π to isolate r^3:
r^3 = 448.9 / ((4/3) * π)
Step 4: Simplify the equation on the right-hand side:
r^3 = 448.9 / (4/3 * 3.14159)
r^3 = 339.29110640781163
Step 5: Take the cube root of both sides to solve for r:
r = ∛339.29110640781163
r ≈ 7.203 inches
Therefore, the approximate radius of the basketball is 7.203 inches.
To find the radius of the basketball, we can rearrange the given formula for volume:
V = 4/3 * π * r^3
Where:
V = Volume of the basketball (given as 448.9 cubic inches)
r = Radius of the basketball (to be found)
First, let's isolate the radius by dividing both sides of the equation by the remaining terms:
V / (4/3 * π) = r^3
Simplifying the right side:
3V / (4π) = r^3
Now, take the cube root of both sides to solve for the radius:
r = cbrt(3V / (4π))
Substituting the given volume:
r = cbrt(3 * 448.9 / (4π))
Calculating this expression will give you the radius of the basketball.