The sweep of the lateral surface of the cylinder is a rectangle diagonal of which = 8 cm

The sweep of the lateral surface of the cylinder is a rectangle diagonal of which = 8 cm and the angle between the diagonal is 60 degrees. find the area of the lateral surface of the cylinder.

The area of ​​the lateral surface of the cylinder is equal to the area of ​​the rectangle – the sweep. Hence, it is necessary to find the area of ​​the rectangle.

Let’s denote the width of the rectangle by a, and the length of the rectangle by b.

The intersection point of the diagonals halves the diagonals of the rectangle. So the half-diagonal of the triangle is:

8/2 = 4 cm.

The diagonals of the rectangle form 4 isosceles triangles. If the angle between the diagonals is 60 °, then the triangle with side b is equilateral (since the other angles will also be 60 °). Means:

b = 4 cm.

Find the width of the rectangle using the Pythagorean theorem:

a² + b² = c²;

a² + 4² = 8²;

a² + 16 = 64;

a² = 48;

a = √48 cm.

Let’s find the area of ​​the rectangle:

S = a * b;

S = √48 * 4;

S = 6√12 * 4;

S = 24√12 cm².

Answer: 24√12 cm²