Respuesta :
The volume of the sphere and the volume of the cylinder can be
expressed in terms of their radius.
Correct response:
- The ratio of the volume of the sphere to the volume of the cylinder is 2 : 3
Methods by which the ratio of the volumes is calculated
The given parameters are;
Radius of the sphere = Radius of the cylinder
Height of the cylinder = Diameter of the sphere
Required:
The ratio of the volume of a sphere to the volume of a cylinder.
Solution:
Let r represent the radius of the sphere, we have;
The diameter of the sphere, D = 2·r
Therefore, the height of the cylinder, h = D = 2·r
The volume of the cylinder is; [tex]V_{cylinder}[/tex] = π·r²·h
[tex]\mathrm{The \ volume \ of \ a \ sphere\ is} \ V_{sphere} = \mathbf{ \dfrac{4}{3} \cdot \pi \cdot r^3}[/tex]
Therefore;
[tex]\mathbf{\dfrac{V_{sphere}}{V_{cylinder}}} = \dfrac{\dfrac{4}{3} \cdot \pi \cdot r^3 }{\pi \cdot r^2 \cdot h} = \dfrac{\dfrac{4}{3} \cdot \pi \cdot r^3 }{\pi \cdot r^2 \times 2 \cdot r} = \dfrac{\dfrac{4}{3} }{2} =\dfrac{4}{6} = \dfrac{2}{3}[/tex]
[tex]\dfrac{2}{3} \ expressed as \ a \ ratio \ is \ 2:3[/tex]
- The ratio of the volume of a sphere to the volume of a cylinder having the same radius, and having a height the same as the diameter of the sphere is 2:3
Learn more about the volumes of solids here:
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