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

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

Answer 2

Answer:

Third option: $35,669 ft^3$

Step-by-step 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:

$V_s= \frac{2}{3} \pi r^3$

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 $\frac{22}{7}$ for $\pi$):

$V=(\frac{22}{7}) (8ft)^2(172ft)+ (\frac{2}{3})(\frac{22}{7})(8ft)^3=35,669 ft^3$