Explanation:
This question has missing diagram, but I'll try to help you either way. We know that the surface area of a sphere is given by:
[tex]S=4\pi r^2 \\ \\ \\ Where: \\ \\ r:\text{radius of the sphere}[/tex]
On the other hand, the volume of a sphere is given by:
[tex]V=\frac{4}{3}\pi r^3[/tex]
1. The hemisphere has a total surface area of:
The total surface area of the hemisphere is half the surface area of a sphere plus the area of the base of the hemisphere which is a circular base with radius r, in other words:
[tex]S_{h}: \text{Surface area of the hemisphere} \\ \\ S_{h}=\frac{4\pi r^2}{2}+\pi r^2 \\ \\ s_{h}=2\pi r^2 + \pi r^2 \\ \\ s_{h}=3\pi r^2[/tex]
2. The hemisphere has a volume of kn cm^3
. Find the value of k.
As I understand this question we want to know what is the value of k given the volume of a sphere, in other words, the volume of a sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]
And the volume of a hemisphere is:
[tex]V_{h}=\frac{\frac{4}{3}\pi r^3}{2}=\frac{2}{3}\pi r^3[/tex]
So the hemisphere has a volume:
[tex]V_{h}=\frac{1}{2}V[/tex]
In other words:
[tex]k=\frac{1}{2}[/tex]
