The volume of a cylinder with a height of 16 and radius of 7 is: 2,460 cubic units.
Volume = 9,651 cubic units.
The radius of this cylinder is 7.0525.
16 pie units squared
The area of the shaded sector is: 245.7 square units.
A sphere with a radius of 16 units has a volume of 17,157.28 cubic units.
V = 4/3(Pi*r3): A sphere with a radius of 16 units has a volume of ≅17,157.28 cubic units.
Radius = cube root of (48/4*pi) = 1.563185284 Check for volume: 4/3*pi*1.5631852843 = 16 cubic units
4/3*Pi*163 = 17,157.28 cubic units
1024pi units2
The volume of a cylinder with a height of 16 and radius of 7 is: 2,460 cubic units.
Surface area of a sphere = 4*pi*radius squared
Volume of sphere: 4/3 times 3.14 times 16^3 = 17148.58667 cubic inches
Volume = 9,651 cubic units.
Vol = 4/3*pi*r3 = 17157 cm3
73,991 cubic units.
Suppose the plane faces of the cylinder lie in the planes that are s units above and below the centre of the sphere. Therefore, the height of the cylinder is 2*s units. Also, by Pythagoras's theorem, the radius of the cylinder, x units, is such that x^2 + s^2 = R^2 = 16 Therefore x^2 = 16 - s^2. Volume of cylinder = pi*x^2*2*s = 2*pi*(16-s^2)*s = 2*pi*(16*s - s^3) Then dV/ds = 0 implies that 2*pi*(16 - 3*s^2) = 0 so s^2 = 16/3 and so s = 4/sqrt(3) The second derivative is -2*pi*6*s which is negative and so the volume is a maximum. When s = 4/sqrt(3), Volume of cylinder = 2*pi*[16 - 16/3]*4/sqrt(3) = 2*pi*32/3*4/sqrt(3) = 256*pi/[3*sqrt(3)] = 256*sqrt(3)*pi/9 = 49.2672*pi approx. The volume of the cylinder is approx 0.5774 times that of the sphere.