Volume of a Cone Practice

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Question 2
Given a cone with a volume of 56.52in3 and height 7in. Find the base radius of the cone. Take π as 3.14.


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A. 3 in3
B. 3 in
C. 2 in3
D. 2 in
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Step by Step Solution 

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Step 1
The picture below shows the cone with height 7in 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 D.

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