The radius of the base of the cylinder is 5cm, the lateral surface area is three times

| May 13, 2021 | education

The radius of the base of the cylinder is 5cm, the lateral surface area is three times the area of one base, find the total surface area and volume of the cylinder.

1. Find the area of ​​the base of the cylinder by the formula S1 = пr ^ 2, where П = 3.14, r is the radius.

S1 = 3.14 × 5 ^ 2 = 3.14 × 25 = 78.5 (cm ^ 2).

2. Find the area of ​​the lateral surface of the cylinder.

S2 = S1 × 3 = 78.5 × 3 = 235.5 (cm ^ 2).

3. The area of ​​the lateral surface of the cylinder is a rectangle, the length of which is equal to the height of the cylinder (a = h), and the width is equal to the length of the circumference bounding the base (b = l).

Let us find the length of the circle that bounds the base of the cylinder by the formula l = 2Пr.

l = 2 × 3.14 × 5 = 31.4 (cm).

4. Since the area of ​​a rectangle is found by the formula S2 = ab, its length can be found by the formula a = S2 / b.

Let us express the length of the rectangle in terms of the circumference of the base.

a = S2 / l.

5. Find the height of the cylinder.

h = a = S2 / l = 235.5 / 31.4 = 7.5 (cm).

6. Find the volume of the cylinder by the formula V = hS1.

V = 7.5 × 78.5 = 588.75 (cm ^ 3).

7. Find the total surface area of ​​the cylinder by the formula S = 2S1 + S2.

S = 2 × 78.5 + 235.5 = 157 + 235.5 = 392.5 (cm ^ 2).

Answer: S = 392.5 cm ^ 2; V = 588.75 cm ^ 3.



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