Two cones are such that the ratio of their volumes is 1 : 10 and ratio of their heights is 2 : 5. What is the ratio of their base radii?

Correct option is B

As we know,
Volume of cone = (1/3) × πr$$^2$$​h
Ratio of height of two cones = h1: h2 = 2 : 5
Ratio of volume of two cone V1 : V2 = (1/3) × π × (r1)$$^2$$​× h1 : (1/3) × π ×(r2)$$^2$$​×h2
=> V1: V2 = (r1)$$^2$$​ × h1 : (r2)$$^2$$​ × h2
=> 1: 10 = (r1)$$^2$$​× 2: (r2)$$^2$$​×5
=> 1/10 = [(r1)$$^2$$ × 2] / [(r2)$$^2$$ × 5] ​​
=> (r1)$$^2$$/(r2)$$^2$$ = 1/4 ​​
=>r1/r2 = √1/4
r1:r2 = 1:2