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(8.5ft)2(2ft) + one over threeπ(2ft)2(13ft − 8.5ft)
π(2ft)2(8.5ft) + one over threeπ(2ft)2(13ft − 8.5ft)
π(8.5ft)2(2ft) + one over threeπ(13ft − 8.5ft)2(2ft)
π(2ft)2(8.5ft) + one over threeπ(13ft − 8.5ft)2(2ft)

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(8.5ft)2(2ft) +  one over threeπ(2ft)2(13ft − 8.5ft)
 π(2ft)2(8.5ft) +  one over threeπ(2ft)2(13ft − 8.5ft)
 π(8.5ft)2(2ft) +  one over threeπ(13ft − 8.5ft)2(2ft)
 π(2ft)2(8.5ft) +  one over threeπ(13ft − 8.5ft)2(2ft)

anonymous · Answer

attachment

welshfella · Answer

does (2ft)2    mean 2 feet squared?

welshfella · Answer

- just making sure

anonymous · Answer

yes

anonymous · Answer

@welshfella

welshfella · Answer

Ok  the volume of the cylindrical part = π r^2 h

where r = radius (which is half the diameter) and h = height

welshfella · Answer

and the volume of the cone  = (1/3) π r^2 h

where r=radius and h = height

welshfella · Answer

now check out the diagram to find these values and plug them into the above formulas

anonymous · Answer

okay im thinking a or b

welshfella · Answer

ok  but try and work the formula out

radius = 1/2 * 4 = 2
and height of the cylinder = 8.5

what is the height of the cone?

welshfella · Answer

cylinder =  π r^2 h  = π * 2^2 * what ?

anonymous · Answer

im finding the volume of the cylinder?

welshfella · Answer

yes  what comes after the 2^2?

welshfella · Answer

h right   what is h?

anonymous · Answer

the volume would be 106.81

anonymous · Answer

h is height

welshfella · Answer

yes and  h = ?

anonymous · Answer

8.5**

welshfella · Answer

right

vol of cyl = π* 2^2 * 8

anonymous · Answer

right

welshfella · Answer

and volume of the cone = 1/3 π 2^2 * h

and h = difference (13 - 8.5)


so which of the choices is correct?

welshfella · Answer

the volumes of the cyl and cone are of course added together

welshfella · Answer

have a close look at a and b.   It is one of those Which one?

welshfella · Answer

putting the volumes together we have
 π* 2^2 * 8.8  +  1/3 π 2^2 * (13 -  8.5)

welshfella · Answer

a or b?

welshfella · Answer

oh a typo - that should be 8.5 not 8.8

anonymous · Answer

a?

welshfella · Answer

a is  π* 8.5^2 * 2 + 1/3 π 2^2 * (13 - 8.5)

welshfella · Answer

check this against what we worked out

welshfella · Answer

is 8.5 the radius and 2 the height??

welshfella · Answer

i gotta go right now
- check out my posts i'm sure you can work it out