A sphere has a volume of 4.44 cubic inches.If the sphere's volume can vary between 3.64 cubic inches and 5.04 cubic inches , how can the radius vary? Round your answer to five
Decimal places.
A)Radius can vary between 0.93219 inch and 1.09691 inches.
B)Radius can vary between 0.21960 inch and 1.61960 inches.
C)Radius can vary between 1.69081 inches and 1.98957 inches.
D)Radius can vary between 1.51481 inches and 1.68837 inches.
E)Radius can vary between 0.95427 inch and 1.06361 inches.

Question

Quizplus · Accepted Answer

The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius.
We know that the volume of the sphere is 4.44 cubic inches.

So, (4/3)πr^3 = 4.44
r^3 = (4.44 × 3)/π
r^3 = 4.48
r = cube root of 4.48 
r = 1.0763 (approx.)

Now, we need to find the range of values for the radius given that the volume can vary between 3.64 cubic inches and 5.04 cubic inches.

Using the same formula, we get:
For V = 3.64, r = cube root of (3.64 × 3)/(4π) ≈ 0.95427
For V = 5.04, r = cube root of (5.04 × 3)/(4π) ≈ 1.06361

So, the radius can vary between 0.95427 inch and 1.06361 inches. 
The closest option to this range is E, which is the answer. The formula for the volume of a sphere is V = (4/3)πr³.
We can rearrange this formula to solve for the radius (r): r = (3V/4π)^(1/3)

Using this formula and the given volume range of 3.64 cubic inches to 5.04 cubic inches, we can find the range of possible radius values:

Radius can vary between ((3*3.64)/(4*3.14159))^(1/3) = 0.95427 inches 
and ((3*5.04)/(4*3.14159))^(1/3) = 1.06361 inches.

Round to five decimal places, the range is:
Radius can vary between 0.95427 inch and 1.06361 inches.

Therefore, the best choice is answer E.

A Sphere Has a Volume of 4