The height of the cylinder is 36 cm, the diameter of its base is 20 cm. How much should the height of the cylinder

The height of the cylinder is 36 cm, the diameter of its base is 20 cm. How much should the height of the cylinder be increased in order for the lateral surface area of the new cylinder to be the full surface of the given one?

First of all, let us find the total surface area of ​​a given cylinder. It is equal to the sum of the areas of its bases and lateral surface:

S = 2πrh + 2πr ^ 2;

r = d / 2;

r = 20/2 = 10 cm;

S = (2 · 3.14 · 10 · 36) + (2 · 3.14 · 100) = 2260.8 + 628 = 2888.8 cm2.

Now calculate the height of the larger cylinder.

The lateral surface area of ​​the larger cylinder is equal to the total surface of the given one:

S (b.p.) 1 = Sp.p .;

S (b.p.) 1 = 2888.8 cm2.

To calculate the height of the larger cylinder, we use the formula for the lateral surface area:

Sb.p. = 2πrh;

h = Sb.p. / 2πr;

h = 2888.8 / (2 3.14 10) = 2888.8 / 62.8 = 46 cm.

Answer: The height of the larger cylinder should be 46 cm