1: Joe has exactly enough paint to paint the surface of a cube whose side length is 2. It turns out that this is also exactly enough paint to paint the surface of a sphere. If the volume of this sphere is {Ksqrt6}/{sqrt(pi)}, then what is K?

2: A pipe with inside diameter 10'' is to carry water from a reservoir to a small town in an arid land. Neglecting the friction and turbulence of the water against the inside of the pipes, what is the minimum number of 2''-inside-diameter pipes of the same length needed to carry the same volume of water to the arid town?

Thanks!

AnonymousConfusedGuy
May 17, 2018

#1**+1 **

2: A pipe with inside diameter 10'' is to carry water from a reservoir to a small town in an arid land. Neglecting the friction and turbulence of the water against the inside of the pipes, what is the minimum number of 2''-inside-diameter pipes of the same length needed to carry the same volume of water to the arid town?

Note that the volume of water carried by one 10 in diameter pipe of some length, L, is :

pi (10/2)^2 * L = 25 L pi units ^3

Note that the volume of water carried by one 2 in diameter pipe of the same length, L, is :

pi (2/2)^2 * L = L pi units^3

So.....we would need 25 times the number of 2 in diameter pipes of some length L to carry the same amount of water as one 10 in diameter pipe of the same length

CPhill
May 17, 2018

#2**+1 **

1: Joe has exactly enough paint to paint the surface of a cube whose side length is 2. It turns out that this is also exactly enough paint to paint the surface of a sphere. If the volume of this sphere is {Ksqrt6}/{sqrt(pi)}, then what is K?

The total surface area of the cube is 6 * 2^2 = 24 units^2

So......for the sphere, we can find the radius as

24 = 4 pi ^ r^2

6/pi = r^2

â[6/pi] = r

So.....the volume of the sphere is

Kâ[6/pi] = (4/3) pi * [ â[6/pi] ] ^3

K = (4/3) pi * â[6/pi]^2

K = (4/3) pi *[ 6 / pi ]

K = (4/3) * 6

K = 8

CPhill
May 17, 2018