Answer:
Third option: [tex]35,669 ft^3[/tex]
Step-by-step explanation:
You need to use the formula for calculate the volume of a cylinder:
[tex]V_c=\pi r^2h[/tex]
Where r is the radius (In this case is 8 feet) and h is the height (In this case is 172 feet).
The formula for calculate the volume of a half sphere is:
[tex]V_s= \frac{2}{3} \pi  r^3[/tex]
Where r is the radius (In this case is 8 feet)
You need to add the volume of the cylinder and the volume of the half-sphere. Then the volume of grain that could completely fill this silo, rounded to the nearest whole number is (Remeber to use [tex]\frac{22}{7}[/tex] for [tex]\pi[/tex]):
[tex]V=(\frac{22}{7}) (8ft)^2(172ft)+ (\frac{2}{3})(\frac{22}{7})(8ft)^3=35,669 ft^3[/tex]
Answer:
The correct answer is third option 35,669 feet³
Step-by-step explanation:
It is given that, Grain silo formed by cylinder with radius 8 feet and height 172 feet and a half sphere on the top
We have to find the volume of cylinder + volume of semi sphere
To find the volume of cylinder
Here r = 8 feet and f cylinder = πr²h
 = (22/7) * 8² * 172
 = 34596.57 ≈ 34597 feet³
To find the volume of hemisphere
here r = 8 feet
Volume of hemisphere = (2/3)πr³
 = (2/3) * (22/7) * 8³
 = 1072.76 ≈ 1073 feet³
To find the total volume
Total volume = volume of cylinder + volume of hemisphere
 = 34597 + 1073
 = 35,669 feet³
The correct answer is third option 35,669 feet³
