Answer:
[tex]r = 3.74cm[/tex]
Step-by-step explanation:
Given
Hemisphere
[tex]Radius = 7cm[/tex]
Cone
[tex]Height = 49m[/tex]
Required
Determine the radius of the cone
First, we calculate the volume (V1) of the hemisphere.
[tex]V_1 = \frac{2}{3}\pi r^3[/tex]
Substitute 7 for r
[tex]V_1 = \frac{2}{3}\pi * 7^3[/tex]
[tex]V_1 = \frac{2}{3}\pi * 343[/tex]
[tex]V_1 = \frac{686}{3}\pi[/tex]
Volume (V2) of a cone is:
[tex]V_2 = \frac{1}{3}\pi r^2h[/tex]
Because the lead is cast into a cone, then they have the same volume.
So, we have:
[tex]\frac{686}{3}\pi = \frac{1}{3}\pi r^2h[/tex]
[tex]686 = r^2h[/tex]
Substitute 49 for h
[tex]686 = r^2 * 49[/tex]
Divide both sides by 49
[tex]r^2 = \frac{686}{49}[/tex]
[tex]r^2 = 14[/tex]
[tex]r = \sqrt{14[/tex]
[tex]r = 3.74cm[/tex]
Hence, the radius of the cone is 3.74cm
