Using Area and Volume Formulas

by Gloria
(Puerto Rico)

A pizza box measures l7 inches long, l6 l/2 inches wide, and 2 inches high. what is the total area of the box and what is the volume?

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May 16, 2010
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by: Karin

Hi Gloria,

You need to find the surface area, which means finding the area of all surfaces on the pizza box. The pizza box has a top and bottom, which will have the same area. It also has a front and back and then 2 sides. We have to find the area of each of those sides.

The area formula for a rectangle is: A = l x w.
Area = length times width.

So, for your cereal box:
We'll first find the area of the top and bottom. The top and bottom is the length and width of the pizza box.
A = l x w
A = 17 x 16.5
A = 280.5 in^2

Now we'll find the area of the front of the box. This is the length and the height is actually the width if it's laid flat.

A = l x w
A = 17 x 2
A = 34 in^2

Now we'll find the area of the sides which is the width and the height.

A = lxw
A = 16.5 x 2
A = 33 in^2

Now we know that we have 2 of each side, so we have to multiply and add them all together

2(top) + 2(front) + 2(sides) = total surface area
2(280.5) + 2(34) + 2(33) = 695 in^2.

The total surface area is 695 in^2.


Now for the volume. The volume formula is:
V = l x w x h (Volume = length times width times height.)

V = l x w x h
V = 17 x 16.5 x 2
V = 561 in^3

Hope this helps!
Karin

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