Question

A grain silo is shown below: Grain silo formed by cylinder with radius 8 feet and height 172 feet and a half sphere on the top What is the volume of grain that could completely fill this silo, rounded to the nearest whole number? Use 22 over 7 for pi. (4 points) 34,597 ft3 11,532 ft3 35,669 ft3 2,146 ft3

Answer 1

The correct answer is third option 35,669 feet³

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

Answer 2

Third option:
`35,669 ft^3`

Explanation:

You need to use the formula for calculate the volume of a cylinder:

`V_c=\pi r^2h`

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:

`V_s= (2)/(3) \pi  r^3`

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
`(22)/(7)` for
`\pi`):

`V=((22)/(7)) (8ft)^2(172ft)+ ((2)/(3))((22)/(7))(8ft)^3=35,669 ft^3`