Answer:
[tex] V = \frac{10}{3} \pi r^2h [/tex]
Step-by-step explanation:
The cone has the following given dimensions:
Radius = r
Height = h
Volume of a cone = ⅓πr²h
The Cylinder has:
Radius = r
Height = 3h
Volume of the cylinder = πr²h = πr²*3h = 3πr²h
Volume of the cement post = volume of Cone + volume of Cylinder
Equation to find total volume of cement post:
V = ⅓πr²h + 3πr²h
[tex] V = \frac{\pi r^2h}{3} + \frac{3 \pi r^2h}{1} [/tex]
[tex] V = \frac{1(\pi r^2h) + 3(3 \pi r^2h)}{3} [/tex]
[tex] V = \frac{\pi r^2h + 9 \pi r^2h}{3} [/tex]
[tex] V = \frac{10 \pi r^2h}{3} [/tex]
[tex] V = \frac{10}{3} \pi r^2h [/tex]
