Calculate the surface area and volume of the cylinder if its height is 10 cm and the base diameter is 6 cm.

1. It is known that 1) the area of ​​the circle (S2) is equal to П * D ^ 2/4;

2) the area of ​​the rectangle (S1) is equal to the product of its length and width;

3) the circumference (P) is equal to the product of the number P and half the diameter;

4) the volume of the cylinder (V) is equal to the product of the area of ​​its base by the height (h).

2. Let’s calculate the surface area of ​​the cylinder.

It consists of the area of ​​a rectangle, the length of which is equal to the perimeter of the base, and the width is equal to the height of the cylinder, and two areas of the base.

S = 2 * S2 + S1.

S2 = P * D ^ 2/4 = 3.14 * 6 ^ 2: 4 = 3.14 * 36: 4 = 28.26 cm ^ 2.

P = P * D / 2 = 3.14 * 6 cm: 2 = 9.42 cm.

S1 = P * h = 9.42 * 6 cm = 56.52 cm ^ 2.

S = 2 * 28.26 + 56.52 = 84.78 cm ^ 2.

3. Let’s calculate the volume of the cylinder.

V = S2 * h = 28.26 * 6 = 169.56 cm ^ 3.

Answer: The surface area of ​​a cylinder is 84.78 square centimeters.

The volume of the cube is 169.56 cubic centimeters.