Math Expression: Volume of a Sphere Practice Question

Given a sphere with a volume of 904.32 in³. Find the radius of the sphere. Take π as 3.14.

Step 1

The picture below shows the sphere with the radius r inches.
Step 2

Since the value of the volume, V and π are given, we can substitute them into the volume of a sphere formula as shown:
Step 3

Now, notice that we can remove the fraction in the equation by multiplying both sides of the equation by 3. This is shown below:
Step 4

We can now continue calculating...
Step 5

Now, we have 12.56r³ = 2712.96. To get a step closer in finding r, we need to remove 12.56 by dividing both sides with 12.56. This is shown below:
Step 6

Now, we have r³ = 216. Since r cube is a multiplication of r three times, we can find r by taking the cube root of 216. This is shown below:
Step 7

Now, the calculated number 6, has no meaning until we include the unit for it. Since volume in unit inch³, r will be in inch. Hence:

r = 6 in
Step 8

Therefore, the answer is D.