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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
JMAP geometry math cone
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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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peter
Asked by peterrep:938
University of Lagos Nigeria
23 June 2020

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judziy
Judziy answeredrep:909
University of Benin Nigeria
23 June 2020
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Volume of cone A, VA = 1/3 πrA2hA

where rA and hA are the radius and height of cone A respectively.

Volume of cone B, VB = 1/3 πrB2hB

where rB and hB 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, rA = 2rB

Also, since the height of cone B is twice the height of cone A, hB = 2hA.

Thus,

hA = hB/2

Therefore, VA = 1/3 π(2rB)2(hB/2)

VA = 1/3 π x 4 x rB2 x hB/2

VA = 4/2 (1/3 πrB2hB)

VA = 2 (1/3 πrB2hB)

But, 1/3 πrB2h= VB

VA = 2VB

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

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