Volume of a Cone Practice

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Question 2

Given a cone with the volume of 56.52in3 and height of 6in. Find the base radius of this cone. Take π as 3.14.

Answer

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Select and check your answer...

A. 3 in3
B. 3 in
C. 2 in3
D. 2 in

Step by Step Solution

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    Step 1

    The picture below shows the cone with the height of 6in and radius r.

    cone with height 7in and base radius r
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    Step 2

    Since the value of the volume, V and π and height, h are given, we can substitute them into the volume of a cone formula as shown:

    substituting the values of V, Pi and h
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    Step 3

    Now, we have 6.28r2 = 56.52. To get a step closer in finding r, we need to remove 6.28 by dividing both sides of the equation with 6.28. This is shown below:

    dividing both sides of the equation with 6.28
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    Step 4

    Now, we have r2 = 9. Since r square is a multiplication of r two times, we can find r by taking the square root of 9. This is shown below:

    square root of 9 is 3
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    Step 5

    Now, the calculated number 3, has no meaning until we include the unit for it. Since volume in unit inch3, r will be in inch. Hence:

    r = 3 in
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    Step 6

    Therefore, the answer is B.

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