An open box whose shape is a cuboid has dimension 9 cm by 7 cm by 6 cm. Find (I) the outer surface of the box (II) the volume of the box

Answer 1

(I) The outer surface of the box can be found by adding up the areas of all six faces.

The dimensions of the box are 9 cm by 7 cm by 6 cm.

The area of the top face is length times width, so it is 9 cm * 7 cm = 63 cm^2.
The area of the bottom face is also 63 cm^2.
The area of the front face is 9 cm * 6 cm = 54 cm^2.
The area of the back face is also 54 cm^2.
The area of the left side face is 7 cm * 6 cm = 42 cm^2.
The area of the right side face is also 42 cm^2.

Adding up all the areas, the total outer surface area of the box is 63 cm^2 + 63 cm^2 + 54 cm^2 + 54 cm^2 + 42 cm^2 + 42 cm^2 = <<63+63+54+54+42+42=318>>318 cm^2.

Therefore, the outer surface area of the box is 318 cm^2.

(II) The volume of the box can be found by multiplying the length, width, and height.

The dimensions of the box are 9 cm by 7 cm by 6 cm.

So the volume of the box is 9 cm * 7 cm * 6 cm = <<9*7*6=378>>378 cm^3.

Therefore, the volume of the box is 378 cm^3.