The ratio of radii of a cylinder to a cone is 1:2. If their heights are equal, then the ratio of their volumes is:

Given:

Radius of cylinder (r_c) = r

Radius of cone (r_cone) = 2r

Height of cylinder = Height of cone = h

Formula used:

Volume of cylinder (V_c) = πr²h

Volume of cone (V_cone) = (1/3)πr²h

Calculation:

Volume of cylinder = πr²h

Volume of cone = (1/3)π(2r)²h

⇒ Volume of cone = (1/3)π(4r²)h

Ratio of volumes = Volume of cylinder : Volume of cone

⇒ Ratio = πr²h : (1/3)π(4r²)h

⇒ Ratio = 1 : (4/3)

⇒ Ratio = 3 : 4

∴ The correct answer is option (3).