If the volume of a spherical ball is 1437 cubic inches, what is the radius?
a
13 inches
b
7 inches
c
5 inches
d
9 inches
d
9 inches
The formula for the volume of a sphere is V = (4/3)πr³, where V is the volume and r is the radius. We are given that the volume of the spherical ball is 1437 cubic inches.
To find the radius, we need to rearrange the formula to solve for r:
V = (4/3)πr³
Divide both sides by (4/3)π:
V / (4/3)π = r³
Now, substitute the given volume of the sphere:
1437 / (4/3)π = r³
Evaluate the right side of the equation:
r³ ≈ 1437 / (4/3)π
simplify further:
r³ ≈ (3/4) * 1437 / π
r³ ≈ 3 * 359.25 / π
r³ ≈ 1077.75 / π
Now, find the cube root of both sides to solve for r:
r ≈ ∛(1077.75 / π)
Using a calculator, evaluate the right side:
r ≈ ∛(344.482)]
r ≈ 6.74 (rounded to two decimal places)
Therefore, the radius of the spherical ball is approximately 6.74 inches.
None of the given options match this result, so none of the options (a, b, c, or d) are correct.
To find the radius of a spherical ball given its volume, you can use the formula for the volume of a sphere:
V = (4/3) * π * r^3
where V is the volume and r is the radius of the sphere.
In this case, the volume of the spherical ball is given as 1437 cubic inches. So, we can set up the equation:
1437 = (4/3) * π * r^3
To find the radius, we need to isolate the r^3 term. First, divide both sides of the equation by (4/3) * π:
1437 / ((4/3) * π) = r^3
Next, take the cube root of both sides to solve for r:
r = ∛(1437 / ((4/3) * π))
Now, let's calculate the value of r:
r ≈ ∛(1437 / ((4/3) * 3.14))
r ≈ ∛(1437 / 4.1867)
r ≈ ∛343.3152
r ≈ 7
Therefore, the radius of the spherical ball is approximately 7 inches.
So, the correct answer is option b) 7 inches.