Answer:
V = 1206.3 [tex]ft^{3}[/tex]
Step-by-step explanation:
This shape is made up of a cylinder on the bottom and a cone on the top. We'll find the volumes of these shapes separately and then add them together.
Volume of a cylinder = area (of the base) x height
Substitute in the formula for the area of a circle.
V(cylinder) = [tex]\pi[/tex][tex]r^{2}[/tex] x h
Substitute in the values for the radius (8) and height (4)
V(cylinder) = [tex]\pi[/tex] x [tex]8^{2}[/tex] x 4
Evaluate using a calculator
V(cylinder) = 804.2477
To the nearest tenth, V(cylinder) = 804.2
Volume of a cone = [tex]\frac{\pi r^{2}h }{3}[/tex]. This is the area of the circular part of the cone ([tex]\pi r^{2}[/tex]), multiplied by the height from the point to the base, all divided by 3.
Substitute in the values for the radius of the circle (8) and the height (6)
V(cone) = [tex]\frac{\pi 8^{2} 6 }{3}[/tex] (On the top it's [tex]\pi[/tex] x [tex]8^{2}[/tex] x 6)
Evaluate using a calculator
V(cone) = 402.1239
To the nearest tenth, V(cone) = 402.1
Total volume = V(cylinder) + V(cone)
= 804.2 + 402.1
= 1206.3 [tex]ft^{3}[/tex]
