surface area and volume please view this tutorial and answer the follow-up questions on loose leaf...
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Surface Area and Volume
Please view this tutorial and answer the follow-up questions on loose leaf to
turn in to your teacher.
Definitions
• Surface area is the sum of the areas of all faces on a three dimensional object.
• Surface area is measured in squared units.
• Volume is the amount of space inside a three dimensional object.
• Volume is measured in cubic units.
General Formulas
Total Surface Area
TSA = 2B + (perimeter of base)(height of prism)
Volume
V = B(height of prism)
B = the area of the base of the prism
Surface AreaSurface area is similar to the amount of wrapping paper needed to wrap a gift.
To find surface area, you must find the 2-D areas of all the faces of the space shape. Add all of the areas together to find the total surface area.
How many faces does a rectangular prism have?
You should have said six.
TopBack
FrontRight
Left
Bottom
Surface AreaFind the surface area of the
rectangular prism.
15 in
6 in4 in
We’re going to have to find the area of all six faces.
15 in 15 in
4 in 4 in
15 in 15 in
6 in 6 in
6 in
6 in
4 in
4 in
Surface AreaFind the surface area of the
rectangular prism.
15 in
6 in4 in
Find the area of all the rectangles. Remember that area for a rectangle
is A = lw.
15 in 15 in
4 in 4 in
15 in 15 in
6 in 6 in
6 in
6 in
4 in
4 in
A=60 in2 A=60 in2 A=90 in2 A=90 in2
A=24 in2
A=24 in2
Surface AreaFind the surface area of the
rectangular prism.
15 in
6 in4 in
Now add up all six areas.
15 in 15 in
4 in 4 in
15 in 15 in
6 in 6 in
6 in
6 in
4 in
4 in
A=60 in2 A=60 in2 A=90 in2 A=90 in2
A=24 in2
A=24 in2
A = 60 + 60 + 90 + 90 + 24 + 24 = 348 in2A = 60 + 60 + 90 + 90 + 24 + 24 =
Surface AreaFind the surface area of the
rectangular prism.
15 in
6 in4 in
You could also use the formula…
A =2(l ×w) + 2(l ×h) + 2(w×h)
A =2(15 ×6) + 2(15 ×4) + 2(6 ×4)
A =348in2
Surface AreaFor a triangular prism, we can substitute into
the general formula to come up with a formula that will work for all triangular prisms.
TSA = 2B + (perimeter of base)(height of prism)
Since the base is a triangle, you can replace B with ½bh. The new formula would be:
TSA = 2(½bh) + (a+b+c)(height of prism)
*a, b, and c are the sides of the triangle
Surface Area
Let’s take a look at an example. Get rid of any sides you don’t need.
18 in
15 in15 in12 in
22 in
TSA = 2(½bh) + (a+b+c)(height of prism)
First, label the triangle.
ac
b
hHeight of
prism
a, b, and c are the sides of the base (triangle).
h is the height of the base (triangle).
Surface Area
Now, plug the values into the formula to solve for the
surface area.
18 in
15 in15 in12 in
22 in
TSA = 2(½bh) + (a+b+c)(height of prism)
ac
b
hHeight of
prism
TSA=216 +1056
TSA =1272in2
VolumeVolume is similar to how much water is inside a plastic water
bottle.
You are finding out how many cubic units are in a 3-D space shape.
To the right, are examples of rectangular prisms broken up into cubic units.
VolumeFind the volume of the
rectangular prism.
15 in
6 in4 in
The first step in finding volume is to find the area of the base (B).
15 in
6 in
B =lwB =15(6)B =90in2
VolumeFind the volume of the
rectangular prism.
15 in
6 in4 in
Next we must take the area of the base and multiply it by the height of the prism.
B =90in2
The formula for finding the volume of any prism is…
where B is the area of the base and h is the height of the prism.
h =4in
V =BhV =BhV =90 ×4V =360in3
Remember that Volume is measured in cubic units.
General Formula for Volume
You can use the following formula to find the volume of any prism. You can customize it to come up with
formulas that work for specific shapes.
V = (area of the base)(height of prism)
V =lwhRectangular Prism:
Triangular Prism: *V =12bhH
*h = height of the triangle; H = height of the prism
Volume of a Triangular PrismLet’s look at our triangular
prism from a previous problem.
18 in
15 in15 in12 in
22 in
V =12bhH
What values would you need to plug in to find the
volume?
18 is the base, 12 is the height of the triangle, and
22 is the height of the prism.
Volume of a Triangular Prism
18 in
15 in15 in12 in
22 in
V =12bhH
V =12(18)(12)(22)
V =2376in3
Volume/Surface Area of a Cylinder
r
h
The formula for the surface area of a cylinder is…
SA =2πr2 + 2πrhThe formula for the volume of a cylinder is…
V =πr2hIf you have a problem where the diameter is given, remember to divide the diameter
by two to get the radius.
Follow-Up Questions
Answer the following questions on loose leafand hand them in to your teacher.
Use 3.14 for pi.
Follow-Up QuestionsFind surface area and volume of the following space shapes.
Don’t forget units.
Follow-Up QuestionsFind surface area and volume of the following space shapes.
Don’t forget units.
cm
cm