In this video you will learn how to find the volume of prisms,and pyramids.
The first thing we want to do is read the word problem, and try to draw a picture. The first problem states," A prism has a square base with a width of 3 cm. It has a volume is 90 cm^3.
A square pyramid has the same width for its base, and the same height as the prism.
What is the volume of the pyramid?
A prism has a squarebase with a side of 3,therefore the volume is 90. A square
pyramid has the same width ,base and height as the prism, what is the volume?
If you have a prism and it is associated with a pyramid what is the ratio? The volume of a prism is calculated by multiplying the base area times height.
The volume of a pyramid is 1/3 base area times height. So if the volume of
the related prism is 90 then all we have to do in order to find the volume of the Pyramid is multiply the volume of the prism by 1/3. Take 90 divided by 3 and
we get 30 cm^3 and that would be the volume of the related Pyramid.
The volume of the pyramid is 30 cm^3 becauseit is 1/3 the volume of the related prism.
Lets look at volume problem number 2
Find the volume of a triangular prism whose base is an equilateral triangle with sides of 4 m and a height of 10 m. Round to the nearest tenth, This time we are finding volume of a triangular prism.
Let’s draw a triangular prism that is equal lateral which means each side is equal 4,4, and 4, and the height ofthe prism is 10 centimeters .So the prism has to be 10 centimeter
Let’s concentrate on this equilateral triangle first. We will find the base area of the pyramid first,
and then we multiply by the height, which is 10.
Here is my equilateral triangle 4 by 4 by 4, and what I will do is draw an altitude down here to find the height for my triangle because my height is 1/2 base times height. The base in this case is 4 and the height is well we have a couple of ways to find the height. We can use the 30-60-90
Inside an equilateral triangle we can drop an altitude because you have created a 30-60-90
triangle. This side is right here is 2 half of the 4, and then you can multiply by the
square root of 3 to get the height so that would be 2 square root 3.
You could also use the Pythagorean theorem
Let’s use the Pythagorean theorem to find the height of the pyramid. This side
is 4, and this side is two, and this height is b.
Take 2^2 + b^2 = 4^2 .So 4 squared is 16 and 2^2 is four and we will solve for b^2
so b^2 is equal to 12 so take the square root of 12 and we get 3.464, and round to 3.5 so
3.5 is the height of the triangular prism.
We now can use the volume formula for a pyramid which ½ base times height.
1/2 times 4 times 3.5 which equals 7 which is our base area. Now just multiply
by the height of the pyramid which is 10. 7 x 10 = 70 which means the volume
is 70 meters cubed and that is the volume of the pyramid.
So you draw a picture,and label it, and find the volume of the pyramid.