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
(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.
Sure! I can help you with that.
I) The outer surface of the box:
To find the outer surface area of the cuboid, we need to calculate the area of each face and then add them together.
The formula for the surface area of a cuboid is:
Surface Area = 2*(Length*Width + Width*Height + Length*Height)
Given dimensions of the cuboid:
Length = 9 cm
Width = 7 cm
Height = 6 cm
Substituting these values into the formula:
Surface Area = 2*(9*7 + 7*6 + 9*6)
= 2*(63 + 42 + 54)
= 2*(159)
= 318 cm²
So, the outer surface area of the box is 318 square centimeters.
II) The volume of the box:
The formula to calculate the volume of a cuboid is:
Volume = Length*Width*Height
Given dimensions of the cuboid:
Length = 9 cm
Width = 7 cm
Height = 6 cm
Substituting these values into the formula:
Volume = 9*7*6
= 378 cm³
So, the volume of the box is 378 cubic centimeters.