A cylindrical beaker with diameter 10 in and height 12 in. is filled with water that is then poured into a rectangular

pan that is 14 in. by 9 in. by 3 in. What is the volume of each solid? Would the water overflow the pan? Is so, what is the

height of the water in the beaker after the pan is filled?

A. The volume of the cylindrical beaker = 942.5 in3.

B. Volume of the pan = 378 in3

C. The water in the cylindrical beaker will over flow the pan.

D. The height of the water in the beaker after the pan is filled is 7.2 in

Step-by-step explanation:

Data given from the question.

Diameter = 10 in

Height = 12 in

Dimension of the pan = 14 in x 9 in x 3 in

Determination of the volume of each solid.

A. Volume of the cylindrical beaker:

Volume = πr2h

Radius (r) = 10/2 = 5 in

Height (h) = 12 in

Volume (V) = ?

V = πr2h

V = π x (5) ^2 x 12

V = 942.5 in3.

The volume of the cylindrical beaker = 942.5 in3.

B. Volume of the rectangular pan

Volume = Length x Width x Height

The dimension for the rectangular pan = volume of the pan = 14 in x 9 in x 3 in

Volume of the pan = 378 in3

C. Since the volume of the cylindrical beaker is higher than that of the pan, the water in the cylindrical beaker will overflow the pan.

D. Determination of the height of the water in the cylindrical beaker after the pan is filled. This is illustrated below.

Let us calculate the volume of the water in the cylindrical beaker after the pan is filled

The volume of the cylindrical beaker = 942.5 in3.

Volume of the pan = 378 in3

Volume of water in the cylinder beaker after the pan is filled = 942.5 - 378 = 564.5 in3

With this new volume, we can calculate the new height of the water as follow:

Volume = 564.5 in3

Radius (r) = 5 in (the radius remains the same)

Height (h) = ?

V = πr2h

h = V/πr2

h = 564.5/π (5) ^2

h = 7.2 in

Therefore, the height of the water in the beaker after the pan is filled is 7.2 in