Given:
For cylinder A:
Radius = 3 unit
Height = 4 unit
For cylinder B:
Radius = 4 unit
Height = 3 unit
To find the ratio of the volume of cylinder A to the volume of cylinder B.
Formula
The volume of a cylinder is,
[tex]V = \pi r^{2} h[/tex]
where, r be the radius and
h be the volume of the cylinder.
Now,
For cylinder A
Putting, r = 3 and h = 4 we get,
Volume [tex]V_{A}[/tex] = [tex]\pi (3^{2} )(4)[/tex]
or, [tex]V_{A} = 36\pi[/tex]
For cylinder B
Putting, r = 4 and h = 3 we get
Volume [tex]V_{B}=\pi (4^{2} )(3)[/tex]
or, [tex]V_{B}= 48\pi[/tex]
Now,
The ratio [tex]\frac{V_{A} }{V_{B}} = \frac{36\pi}{48\pi}[/tex]
or, [tex]\frac{V_{A} }{V_{B}} = \frac{3}{4}[/tex]
Hence,
The ratio of the volume of Cylinder A to the volume of Cylinder B is [tex]\frac{3}{4}[/tex]. Option A
