Option B:
Volume of composite figure is [tex]\frac{2}{3} \pi r^{3}[/tex].
Solution:
Composite figure is made of cylinder and cone.
Radius of cylinder and cone are equal.
Radius of cone and cylinder = r
Height of cylinder and cone are equal to the radius.
Height of cylinder and cone (h) = r
Volume of cylinder = [tex]\pi r^2h[/tex]
[tex]=\pi r^2 \times r[/tex]
[tex]=\pi r^3[/tex]
Volume of cone = [tex]\frac{1}{3} \pi r^2h[/tex]
[tex]$=\frac{1}{3} \pi r^2 \times r[/tex]
[tex]$=\frac{1}{3} \pi r^3[/tex]
Volume of composite figure = Volume of cylinder - Volume of cone
[tex]$= \pi r^{3}-\frac{1}{3} \pi r^{3}[/tex]
Take LCM for 1 and 3 and make the denominator same.
[tex]$= \frac{3}{3} \pi r^{3}-\frac{1}{3} \pi r^{3}[/tex]
[tex]$= \frac{3-1}{3} \pi r^{3}[/tex]
[tex]$= \frac{2}{3} \pi r^{3}[/tex]
Volume of composite figure is [tex]\frac{2}{3} \pi r^{3}[/tex].
Option B is the correct answer.
