The sides of the rectangle are 4 cm and 5 cm. Find the surface area and volume of the body obtained

The sides of the rectangle are 4 cm and 5 cm. Find the surface area and volume of the body obtained by rotating the rectangle around its smaller side.

When the rectangle rotates around one of its sides, a cylinder is formed.

The height of the cylinder will be equal to the scarlet side of the rectangle (4 cm), and the radius of the circle of the cylinder larger than the sides of the rectangle (5 cm)

Let’s calculate the volume of the resulting cylinder.

V = π x R ^ 2 x h.

Where R = 5 cm, the length of the longer side of the rectangle.

h – 4 cm, the length of the shorter side of the rectangle.

π – number pi = 3.14.

V = π x 5 ^ 2 x 4 = 100 x π cm3.

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

S = 2 x Sо + Sb.

Where So is the base area.

Sb – lateral surface area.

Knowing the volume of the cylinder and the height, you can calculate the area of ​​the base of the cylinder.

Sо = V / h = (100 x π) / 4 = (25 x π) cm2.

The lateral surface area of ​​the cylinder is:

Sb = 2 x π x R x h = 2 x π x 5 x 4 = 40 x π cm2.

S = 2 x Sо + Sb = (2 x 25 x π) + 40 x π = 90 x π.

Answer: The volume is (100 x π) cm3. The area is (90 x π) cm2.