Question

A right angled triangle has one of its acute angles equal to 30degrees. The volume of the cone generated by revolving the triangle about the side opposite to 30degrees angle is A1 and the volume of the cone generated by revolving the triangle about the side adjacent to 30degrees angle is A2. Then A1:A2 = ______.

a)pi/root3
b) root3
c) root3/pi
d) 1/root3

Answer 1

The volume of a cone is: 1/3 (pi r^2) (h) where;

r = sqrt(3), and h = 1 for A1

r = 1 and h = sqrt(3) for A2

Answer 2

A1:A2 = 1/(sqrt(3)/3) = 3/sqrt(3) = sqrt(3); my pick is b

Answer 3

Assume the side opposite 30 degrees is of length 1 then the hypotenuse is 2 (trig) and the other side must be root3.

The cone area is 1/3 of area of base (circle of radius root3 or 1 respectively) by height (1 or root3 respectively).

I think you can manage those calculations....