Question

A company that manufactures storage bins for grains made a drawing of a silo. The silo has a conical base, as shown below:
Which of the following could be used to calculate the total volume of grains that can be stored in the silo?

π(2ft)2(8ft) + one over threeπ(2ft)2(9.5ft − 8ft)
π(8ft)2(2ft) + one over threeπ(2ft)2(9.5ft − 8ft)
π(2ft)2(8ft) + one over threeπ(9.5ft − 8ft)2(2ft)
π(8ft)2(2ft) + one over threeπ(9.5ft − 8ft)2(2ft)

Answer 1

@AZ

Answer 2

ah, that image was confusing for a sec but the bottom part is a cone

So think of a shape like this

Answer 3

We want to find the total volume so that means volume of cylinder + volume of cone

do you know the formulas for volume of a cylinder or cone?

Answer 4

V= pi 2 h?

Answer 5

And for a cone its V= 1/ 3h pi r 2

Answer 6

yeah

For a cylinder
V = \(\pi r^2 h\)

For a cone
V = \(\dfrac{1}{3} \pi r^2h\)

Answer 7

so for the cylinder, we know the diameter is 4

what is the radius?

and the height of the cylinder is 8 feet

Answer 8

Do you have to calculate the cone and the cylinder seperately?

Answer 9

yes, and we add them together to find the total volume

Answer 10

Basically we break up the complex shape into shapes we know and calculate the volume

and the total volume is the volume of each part all added together

Answer 11

Right ok

Answer 12

So you only have to plug in the numbers, you don't really need to calculate the final answers

the radius of the cone is going to be the same radius as the cylinder

diameter = radius * 2

we know the diameter is 4 so what is the radius?

Answer 13

and the height of the cone is the difference of the total height and the cylinder's height

we know the entire thing is 9.5 feet
and the cylinder has a height of 8

so the height of the cone is what gets added to the cylinder's height to give you the total height of 9.5

so the height of the cone is 9.5 - 8 = ??

Answer 14

Uh 1.5

Answer 15

Wait how do you figure out the radius?

Answer 16

The radius is half of the diameter

Answer 17

Oh 2 then

Answer 18

Volumes 6.28 then rounded to 6.3

Answer 19

exactly so total volume = volume of cylinder + volume of cone

total volume = \(\pi r^2h_1 + \dfrac{1}{3} \pi r^2 h_2\)

plug in r = 2
the first height is 8
the second height is 1.5

Answer 20

Look at your answer choices, we don't need to actually calculate the volume

we just need to set it up

and I realized that we don't need to do the subtract either

the height of the cone should have just been left as (9.5 - 8)

Answer 21

Oh so is it the first option?

Answer 22

Yup!

Answer 23

Alright great