288π cm³
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volume of sphere: 4/3 * π * radius³
⇒ 4/3 * π * (6)³
⇒ 4/3 * 216 * π
⇒ 288π
The overall volume is the sum of the volume of a cylinder of height 5'9" and diameter 3'6", and a sphere of diameter 3'6" (two hemispheres = full sphere).
Volume of the cylinder = (area of the base) x (height) = pi * (diameter/2)^2 * 5.75ft = 3.1415 * (3.5ft/2)^2 * 5.75 ft = 55.32 ft^3
Volume of the sphere = 4/3 * pi * (3.5ft)^3 / 8 = 22.45 ft^3
Total volume = (Volume of cylinder) + (Volume of sphere) = (55.32 + 22.45) ft^3 = 77.77 ft^3
Your answer would be 41.56x
I believe you are asking in how many ways they can sit. If so:
The 1st can sit anywhere: he has only 1 way to sit
The 2nd can sit in 11 ways, since one seat is already occupied
The 3rd can sit in 10 ways, since 2 seat are already occupied
The 4th can sit in 9 ways, since 3 seat are already occupied
The 5th can sit in 8 ways, since 4 seat are already occupied
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The 12th can sit in 1 way, since11 seat are already occupied
General formula for a circular table:
Number of ways they n persons can be seated: (n-1)!
and the 12 can be seated in (12-1)! = 11! = 39,916,800 ways.
This is called circular permutation
Lines k and n are perpendicular
The slope of line k is -6
Fact: The product of slopes of two perpendicular lines = -1
So the slope of line n = -1 ÷ -6 = 1/6
The correct choice is 'D.'
