Volume of a Sphere Practice

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Question 1

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


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Select and check your answer...

A. 10 in3
B. 10 in
C. 6 in3
D. 6 in

Step by Step Solution

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    Step 1

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

    sphere with the radius r
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    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:

    substituting the values of V and Pi
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    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:

    solving for r
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    Step 4

    We can now continue calculating...

    solving for r
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    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:

    dividing both sides of the equation with 12.56
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    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:

    cube root of 216 is 6
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    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
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    Step 8

    Therefore, the answer is D.