0
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.
Wiki User
∙ 9y ago
Add your answer:
Earn +20 pts
What is the volume of a sphere with radius of 4 in?
268.08 cubic inches.
What is the volume of a sphere that has a radius of 6 inches?
Volume of a sphere = 4/3*pi*radius3 Volume = 4/3*pi*63 = 904.7786842 cubic inches A+: 904
What is the volume of sphere if radius is 4 inches?
V = 268.1 cubic inches.
What is the volume of a sphere with a radius of 6 in?
Volume of a sphere = 4/3 * pi * r3 Volume of a sphere = 4/3 * pi(6 in)3 = 905 cubic inches ============
What is thevolume of a sphere with the radius of 4in?
Volume of a sphere = 4/3*pi*radius3 Volume = 268.0825731 or 268 cubic inches
If the radius of a sphere is 4 inches what is its volume?
The volume of a sphere is V=(4/3) pi r 3 so using the radius of 4 and pi to be 3.14 V= (4/3) x 3.14 x 4 3 V=(4/3) x 3.14 x 64 V = 267.946667 7 cubic inches The volume of a sphere with a 4 inch radius is 2.46667 cubic inches.
What is the volume of a sphere that has a radius of 45 inches?
381703.5074 inches cubed Volume=(4/3)*pi*radius cubed So Volume = (4/3)*pi*45^3=381703.5074
What is the approximate volume of a sphere with a radius of 11 inches?
Volume = 4/3*pi*r3 = 5575.3 cubic inches
What is the volume of this sphere that has a radius of 6 inches?
Volume = 4/3*pi*63 = 904.7786842 or about 905 cubic inches
What is the volume of a sphere with a radius of 4 centimeters?
The volume of a sphere with a radius of 4cm is about 268cm3
What is the volumes of a sphere that has a radius of forty five inch?
Volume of a sphere = 4/3*pi*radius3 Volume = 381703.5074 cubic inches
What is the volume of a sphere with a radius of 6 inches?
Volume =4/3*pi*r3 Volume = 4/3(pi)(6 in)3 = 904.8 cubic inches ===============
