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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

User Poorva
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Answer:

The volume of cone A is twice the volume of cone B.

Explanation:

The formula that is used to find the volume of a cone is given by :


V=(1)/(3)\pi r^2 h

Where

r is radius of cone and h is height

ATQ,

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.


r_A=2r_B\ \text{and}\ h_B=2h_A

or


(r_A)/(r_B)={2}\ \text{and}\ (h_A)/(h_B)=(1)/(2)

Taking ratios of their volume,


(V_A)/(V_B)=(1/3\pi r_A^2h_A)/(1/3\pi r_B^2h_B)\\\\(V_A)/(V_B)=((r_A)/(r_B))^2* (h_A)/(h_B)

So,


(V_A)/(V_B)=((r_A)/(r_B))^2* (h_A)/(h_B)\\\\(V_A)/(V_B)=(2)^2* (1)/(2)\\\\(V_A)/(V_B)=2\\\\V_A=2V_B

The volume of cone A is twice the volume of cone B.

User Vii
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