A cylinder container with a 3 in. diameter and a 8 in. height is completely filled with water. all of its contents are poured into another cylindrical container that is 2 in. tall. if the water completely fills the second container, what is the container's diameter?



Answer :

As per the given data of the cylinder container, first cylinder with diameter 3 in and height 8 in completely filled with water and poured into another cylinder of height 2 in then diameter of another cylinder is 6 in..

As given in the question,

Diameter of first cylinder = 3 in.

Radius of first cylinder 'r'= (3/2) in.

Height of first cylinder 'h'= 8 in.

Volume of first cylinder = πr²h

                                    = π ×( 3/2)² × 8

                                    = 18π in³.

Height of second cylinder = 2 in.

let 'R' be the radius of second cylinder

All the contents of first cylinder poured into second cylinder

Volume of first cylinder = Volume of second cylinder

⇒18π = π (R)² (2)

⇒(R)² = 9

⇒ R = 3

Diameter of the second cylinder = 2(R)

                                                   = 6 in.

Therefore, for the given data of the cylinder container, first cylinder with diameter 3 in and height 8 in completely filled with water and poured into another cylinder of height 2 in then diameter of another cylinder is 6 in..

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