Find the length of ad in the diagram shown
2 answers:
Let as consider two triangles ABE and ACD
As we can see these two triangles ABE and ACD are similar triangles
Hence the ratio of sides must be equal
So
Now let AE = x
So plugging all the values we get
AB= 5 , AC= 11 , AE =x , AD = x+9
Cross multiplying we get
5(x+9) = 11(x)
Simplifying
5x +45 = 11x
Subtract 5x from both sides
45 = 6x
Divide both sides by 6
x= 45/6 = 7.5
Hence AE = 7.5
But we have to find the length of AD
AD = AE+ED = 7.5 + 9 = 16.5
AD= 16.5
Option D is the answer
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Remark
All Cavaliere's principle says is that a slanted cylinder (for example) has the same volume as a cylinder with perpendicular parallel lines that the cylinder is sitting on.
I little known or maybe not a well emphasized fact is that the base is the same all the way up the cylinder. The coin picture below shows that. The basic formula for a Cavaliere cylinder is the same as for an ordinary cylinder.
See picture below
Formula
V = B * H
Sub and Solve
V = 1024
r = 8
p=3.14
V = pi*r^2 * h
1024 = 3.14*8^2 * h combine the right side.
1024 = 3.14*64 *h
1024 = 200.96 * h divide by 200.96
1024/200.96 = h
You are only getting 5 inches.
None of your answers work.The conversion to meters is going to give you an even smaller number. If you add a comment, I'll come back and edit this question.
All Cavaliere's principle says is that a slanted cylinder (for example) has the same volume as a cylinder with perpendicular parallel lines that the cylinder is sitting on.
I little known or maybe not a well emphasized fact is that the base is the same all the way up the cylinder. The coin picture below shows that. The basic formula for a Cavaliere cylinder is the same as for an ordinary cylinder.
See picture below
Formula
V = B * H
Sub and Solve
V = 1024
r = 8
p=3.14
V = pi*r^2 * h
1024 = 3.14*8^2 * h combine the right side.
1024 = 3.14*64 *h
1024 = 200.96 * h divide by 200.96
1024/200.96 = h
You are only getting 5 inches.
None of your answers work.The conversion to meters is going to give you an even smaller number. If you add a comment, I'll come back and edit this question.