The ratio of volume of a cone and a hemisphere of same base radius and height is?

1/2

Step-by-step explanation:

Since it is given that the cone and the hemisphere have the same height, and since the height of a hemisphere would be equal to its radius, the cones height must also be equal to its base radius.

With this information we can use the respective volume formulas.

Hemisphere:  πr^3

Cone:  πhr^2

Since h (height) = r we can say the cone volume equals:

πr^3

Now to find the ratio we divide the cone volume equation by the hemisphere volume equation

pi and r^3 cancels out from the division and we are left with

ratio = (1/3)/(2/3)

ratio = 1/2