Answer:
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: [tex]\frac{2}{3}[/tex]πr^3
Cone: [tex]\frac{1}{3}[/tex]πhr^2
Since h (height) = r we can say the cone volume equals:
[tex]\frac{1}{3}[/tex]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
