Question

!!!!!СРОЧНО!!!!!! Прямокутник, сторони якого 2 см і 4 см,обертають навколо меншої сторони. Назвати,чому дорівнює радіус, висота циліндра. Знайтиповну поверхню циліндра.

Answer 1

Ответ:

h=2см

R=4см

Sпол=48π см²

Объяснение:

Цилиндр

h=2см

R=4см

Sбок=2πRh=2π*2*4=16π см²

Sосн=πR²=4²π=16π см²

Sпол=Sбок+2*Sосн=16π+2*16π=16π+32π=

=48π

Answer 2

Problem Analysis

We are given a rectangle with sides measuring 2 cm and 4 cm. The rectangle is rotated around its shorter side. We need to determine the radius and height of the resulting cylinder, as well as find the total surface area of the cylinder.

Solution

To find the radius of the cylinder, we need to consider that the shorter side of the rectangle is the circumference of the base of the cylinder. The formula to calculate the radius (r) from the circumference (C) is:

r = C / (2 * π)

In this case, the circumference is equal to the length of the shorter side of the rectangle, which is 2 cm. Therefore, the radius of the cylinder is:

r = 2 cm / (2 * π) = 1 / π cm

To find the height of the cylinder, we need to consider that the longer side of the rectangle is equal to the height of the cylinder. Therefore, the height of the cylinder is:

h = 4 cm

To find the total surface area of the cylinder, we need to consider the formula:

Total Surface Area = 2πr(r + h)

Substituting the values we found earlier, we get:

Total Surface Area = 2π(1 / π cm)(1 / π cm + 4 cm)

Simplifying the expression, we get:

Total Surface Area = 2π(1 / π cm)(1 / π cm + 4 cm) = 2π(1 / π cm)(1 / π cm + 4 cm) = 2π(1 / π cm)(1 + 4π cm) = 2(1 + 4π) cm²

Therefore, the total surface area of the cylinder is 2(1 + 4π) cm².

Summary

In summary, the radius of the cylinder is 1 / π cm, the height of the cylinder is 4 cm, and the total surface area of the cylinder is 2(1 + 4π) cm².

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