Video: Finding the Total Surface Area of a Rectangular Prism in a Real-World Context

James has a fish tank made of glass without a lid. It is 80 cm long, 75 cm wide, and 50 cm high. How much glass was used to make it?

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Video Transcript

James has a fish tank made of glass without a lid. It is 80 centimetres long, 75 centimetres wide, and 50 centimetres high. How much glass was used to make it?

We can start by sketching this fish tank. If we label the fish tank, it’s 80 centimetres long, 75 centimetres wide, and 50 centimetres high. And we’re asked how much glass was used to make this fish tank. Since the tank does not have a lid, there are five sides of glass instead of six: the base, the two sides on the left and right, and the two sides on the front and back. To find out how much glass was used, we’ll need to find the area of all five of these pieces.

And so, we remember that it is 80 centimetres long, 75 centimetres wide and 50 centimetres tall. We can mark in yellow all the lines that are 80 centimetres long. Let’s mark in pink all the places that would measure 75 centimetres. And the sides remaining in blue will all be the height of 50 centimetres. To find the area of a rectangle, we multiply its length times its width. These two spaces measure 75 by 50. So we multiply 75 times 50 to find its area. And we find that this space measures 3750 centimetres squared, which will be true for both sides.

We can also consider the area of the front and the back. These pieces measure 80 centimetres by 50 centimetres. So we multiply 80 by 50 to find the area. And we find the front and back measures 4000 centimetres squared. And finally, we have the base, which measures 80 centimetres by 75 centimetres. So we multiply those values together, which gives us the value of 6000 centimetres squared.

To find how much glass this fish tank is made of, we have to add all five of these areas together. 4000 plus 4000 plus 3750 plus 3750 plus 6000 equals 21500 centimetres squared. And so, we say that this fish tank is made of 21500 centimetres squared of glass. We’ve just found the surface area of this fish tank.

The surface area is the total area of a three-dimensional object. This fish tank was made up of five rectangles together. And so, by finding the area of each of those and adding them together, we found the surface area of James’s fish tank.

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