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Jaden is comparing two cones. The radius of the base of cone A is twice as large as the radius of the base of cone B. The height of cone B is twice the height of cone A. The volume of cone A is

1) twice the volume of cone B

2) four times the volume of cone B

3) equal to the volume of cone B

4) equal to half the volume of cone B

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Volume of cone A, V_{A} = 1/3 πr_{A}^{2}h_{A}

where r_{A} and h_{A} are the radius and height of cone A respectively.

Volume of cone B, V_{B} = 1/3 πr_{B}^{2}h_{B}

where r_{B} and h_{B} are the radius and height of cone B respectively.

Since the radius of the base of cone A is twice as large as the radius of the base of cone B, r_{A} = 2r_{B}

Also, since the height of cone B is twice the height of cone A, h_{B} = 2h_{A}.

Thus,

h_{A} = h_{B}/2

Therefore, V_{A} = 1/3 π(2r_{B})^{2}(h_{B}/2)

V_{A} = 1/3 π x 4 x r_{B}^{2} x h_{B}/2

V_{A} = 4/2 (1/3 πr_{B}^{2}h_{B})

V_{A} = 2 (1/3 πr_{B}^{2}h_{B})

But, 1/3 πr_{B}^{2}h_{B }= V_{B}

V_{A} = 2V_{B}

Hence, the volume of cone A is twice the volume of cone B

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