Option C
The ratio for the volumes of two similar cylinders is 8 : 27
<h3><u>
Solution:</u></h3>
Let there are two cylinder of heights "h" and "H"
Also radius to be "r" and "R"

Where π = 3.14 , r is the radius and h is the height
Now the ratio of their heights and radii is 2:3 .i.e

<em><u>Ratio for the volumes of two cylinders</u></em>

Cancelling the common terms, we get

Substituting we get,



Hence, the ratio of volume of two cylinders is 8 : 27
Answer:
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By using exponent properties, we will get the simplified expression:

<h3>
How to simplify the given expression?</h3>
Here we have the expression:

Remember the exponent properties:

And:

So using these two properties, we can rewrite:

So we conclude that the completely simplified expression is:

If you want to learn more about exponents:
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Answer:
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Step-by-step explanation:
Answer:
Step-by-step explanation:
Picture 1
In right triangle ABC,
Side AB is the opposite side of angle C.
Picture 2
In triangle MKL,
tan(∠M) = 
= 
= 
Option (1) is the answer.
Picture 3
In ΔXYZ,
sin(∠Z) = 
= 
For the length of XY we will apply Pythagoras theorem in ΔXYZ,
XZ² = XY² + YZ²
XY² = XZ² - YZ²
= (40)² - (32)²
XY = √576
= 24
sin(Z) =
sin(Z) =
Picture 4
In right triangle DEF,
Cos(D) = 
= 
= 
= 
Picture 5
In ΔABC,
tan(63°) = 
tan(63°) = 
AB = 
AB = 
AB = 4.0762 ≈ 4 m
Option (3) will be the answer.