The diagonal of the rectangle is 10 cm and forms a 30 ° angle with the larger side. find the surface area

The diagonal of the rectangle is 10 cm and forms a 30 ° angle with the larger side. find the surface area of the body obtained by rotating a given rectangle around the larger side

If you rotate this rectangle around the larger side, you get a cylinder whose height is equal to the larger side of the rectangle, and the radius is equal to the smaller side.

Since the diagonal of the rectangle is 10 cm and forms an angle of 30 degrees with the larger side, we find the height and radius of the cylinder:

h = 10 * cos 30ᴼ = 5 * √ 3.

r = 10 * sin 30ᴼ = 10 * 1/2 = 5.

The total surface area of the cylinder is:

S = 2 * π * r * h + 2 * π * r²,

S = 2 * π * 5 * 5 * √3 + 2 * π * 5²,

S = 50 * π * (√3 + 1),

S ≈ 428.8 cm².

Answer: S ≈ 428.8 cm².