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Answer:
Volume:
Ratio:
Step-by-step explanation:
First of all, we need to find the volume of the hemispherical tank.
The volume of a sphere is given by:
where
r is the radius of the sphere
V is the volume
Here, we have a hemispherical tank: a hemisphere is exactly a sphere cut in a half, so its volume is half that of the sphere:
Now we want to find the ratio between the volume of the hemisphere and its surface area.
The surface area of a sphere is
For a hemisphere, the area of the curved part of the surface is therefore half of this value, so . Moreover, we have to add the surface of the base, which is
. So the total surface area of the hemispherical tank is
Therefore, the ratio betwen the volume and the surface area of the hemisphere is
To find the cofactor of
We cross out the Row and columns of the respective entries and find the determinant of the remaining matrix with the alternating signs.
Therefore in increasing order, we have;