The circumference of the base of the cylinder is 3. The lateral area is 6. Find the height and surface area of the cylinder.

| February 24, 2021 | education

L = 3.

S side = 6.

h -?

Floor -?

1. The area of ​​the side surface Sside of the cylinder is determined by the formula: Sside = L * h, where L is the circumference of the base of the cylinder, h is the height of the cylinder.

h = S side / L.

h = 6/3 = 2.

2. The total surface area of ​​the cylinder Spol is determined by the formula: Spol = Sbok + 2 * Sb, where Sb is the area of ​​the circle at the base of the cylinder.

3. The area of ​​the circle Ssc is determined by the formula: Sosn = п * R ^ 2, where R is the radius of the cylinder base, п is the number pi.

4. We find the radius of the base of the cylinder R, knowing the length of its circumference L.

L = 2 * п * R.

R = L / 2 * P.

Sosn = P * (L / 2 * п) ^ 2 = L ^ 2/4 * п.

5. The formula for finding the area of ​​the full surface of the cylinder S floor will have the form: S floor = S side + 2 * L / 4 * п = S side + L ^ 2/2 * п.

Spol = 6 + (3) ^ 2/2 * 3.14 = 7.43 = 7.4.

Answer: h = 2, Spol = 7.4.



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