Question

Volumes of a perpendicular circular cone A is thrice the volume of perpendicular circular cone B, the height of cone B is the thrice of height of cone A . the ratio of radius of A to radius of B

Answer 1

We know that, Volume of right circular cone = ⅓πr²h

Given that Volume of A is the Volume of B. V(A) = 3V(B)

Also, Height of Cone B is thrice the height of A.
h(B) = 3h(A) .
Let the height of A be h, and height of B be H.
H = 3h

Now, We need to find ratio of radius. Let the radius of A be r, and Radius of B be R.

Now,
Volume of A = 3 ( Volume of B)
1/3π(r)²[h] = 3 ( 1/3πR²H)

1/3 and π of both sides cancels out.

Now,
r²h = 3R²H

We apply H = 3h .
r²/R² = 3H/h
r²/R² = 9h/h .
r²/R² = 9/1
r² :R² = 9 : 1
r : R = √9 : √1
r : R = 3 : 1 .

Therefore the Ratio of radii ( Radius of A to radius of B) = 3 : 1 .

Hope you are helped!