The volume of solid B cylinder is 9000π cubic units.
A cylinder is a 3-D solid figure that has two identical circular bases joined by a curved surface at a fixed distance from the center, that is the height of the cylinder.
For the given situation,
Cylinder A:
Let the radius of cylinder A be r1 = 12 inches
Let the height of cylinder A be h1
The volume of the cylinder A, V1 = 4608 π cubic inches
Cylinder B:
Let the radius of cylinder A be r2 = 15 inches
Let the height of cylinder A be h2
The volume of the cylinder A, V2
The formula of volume of cylinder is
[tex]V=\pi r^{2}h[/tex]
For cylinder A,
⇒ [tex]4608\pi =\pi (12)^{2}h1[/tex]
⇒ [tex]h1=\frac{4608}{144}[/tex]
⇒ [tex]h1=32[/tex]
Cylinder A and cylinder B are similar, so
[tex]\frac{h1}{h2} =\frac{r1}{r2}[/tex]
⇒ [tex]\frac{32}{h2} =\frac{12}{15}[/tex]
⇒ [tex]h2=\frac{(32)(15)}{12}[/tex]
⇒ [tex]h2=40[/tex]
Volume of cylinder B is
⇒ [tex]V=\pi (15)^{2}(40)[/tex]
⇒ [tex]V=9000\pi[/tex]
Hence we can conclude that the volume of solid B cylinder is 9000π cubic units.
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