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Question

Manoj has a set of blocks that are of the same height. The cone shaped block has a volume of 125 cubic inches. The sphere-shaped block has a volume of 250 cubic inches. What do you know about the radius of the base cone – shaped block?

hintHint:

Since the blocks are of same height, the height of sphere-shaped block is the diameter of the block. So, the diameter of sphere block is equal to the height of cone block. Then we form two equations using the given information and solve the system of equations.

The correct answer is: The radius of the cone shaped block is (35156.25/π^2 )^(1/6).


    Explanations:
    Step 1 of 2:
    Volume of cone shaped block = 1 third pi r squared h ,  r = base radius and h = height
    Volume of sphere-shaped block =  4 over 3 pi open parentheses h over 2 close parentheses cubed,  h = diameter of the block
    Given,4 over 3 pi open parentheses h over 2 close parentheses cubed equals 250
    not stretchy rightwards double arrow h cubed equals 250 cross times 3 over 4 cross times 1 over pi cross times 8 
    not stretchy rightwards double arrow h cubed equals 1500 over pi
    Step 2 of 2:
    Also given, 1 third pi r squared h equals 125
    not stretchy rightwards double arrow 1 over 27 pi cubed r to the power of 6 h cubed equals 125 cubed comma text  taking cube on both sides  end text
    not stretchy rightwards double arrow r to the power of 6 equals 125 cubed cross times 27 cross times 1 over pi cubed cross times pi over 1500 comma text  putting  end text h cubed equals 1500 over pi
    not stretchy rightwards double arrow r to the power of 6 equals fraction numerator 35156.25 over denominator pi squared end fraction
    not stretchy rightwards double arrow r equals open parentheses fraction numerator 35156.25 over denominator pi squared end fraction close parentheses to the power of 1 divided by 6 end exponent
    Final Answer:
    The radius of the cone shaped block is open parentheses fraction numerator 35156.25 over denominator pi squared end fraction close parentheses to the power of 1 divided by 6 end exponent .

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