Question

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The ratio of the surface areas of two similar cylinders is 16/25. The radius of the circular base of the larger cylinder is 0.5 centimeters.

What is the radius of the circular base of the smaller cylinder?

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The radius of the smaller cylinder's circular base is centimeters.

Answer 1

The radius of the smaller cylinder's circular base is 0.4 centimeters.

To solve the problem, we use the fact that the ratio of the surface areas of two similar cylinders is equal to the square of the ratio of their corresponding radii. Let r1 and r2 be the radii of the smaller and larger cylinders, respectively. Then, we have:

(surface area of larger cylinder) / (surface area of smaller cylinder) = (r2^2 * 2πh) / (r1^2 * 2πh) = r2^2 / r1^2

Given that the ratio of the surface areas is 16/25, we have:

16/25 = r2^2 / r1^2

Taking the square root of both sides, we get:

4/5 = r2 / r1

Substituting r2 = 0.5 cm, we get:

4/5 = 0.5 / r1

Solving for r1, we get:

r1 = 0.4 cm

Explanation: