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Margarita [4]
3 years ago
5

Question 10 pls help

Mathematics
1 answer:
Ivenika [448]3 years ago
3 0

Answer:

D

Step-by-step explanation:

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2. The ratio of radii of two cylinders is 1:2 and heights are in the ratio 2:3. Find the ratio of their volumes.
Savatey [412]

Answer: \frac{1}{6} or 1:6

Step-by-step explanation:

The volume of a cylinder can be found with the following formula:

V=\pi r^2h

Where "r" is the radius and "h" is the height of the cylinder.

In this case, let be:

- V_1 the volume of one of this cylinders and V_2 the volume of the other one.

- r_1 the radius of the first one and r_2 the radius of the other cylinder.

- h_1 the height of one of them and h_2 the height of the other cylinder.

Then:

V_1=\pi r_1^2h_1\\\\V_2=\pi r_2^2h_2

Therefore, you know this:

\frac{V_1}{V_2} =\frac{\pi r_1^2h_1}{\pi r_2^2h_2}

Simplifying, you get:

\frac{V_1}{V_2} =\frac{ r_1^2h_1}{ r_2^2h_2}

Now, knowing the ratios given in the exercise, you can substitute them into the equation:

\frac{V_1}{V_2} =\frac{1^2*2}{ 2^2*3}

Evaluating, you get:

\frac{V_1}{V_2} =\frac{2}{ 4*3}\\\\\frac{V_1}{V_2} =\frac{2}{12}\\\\\frac{V_1}{V_2} =\frac{1}{6}

4 0
3 years ago
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