The axial section of the cylinder is a square, the diagonal length of which is 36 cm.
| September 21, 2021 | education
The axial section of the cylinder is a square, the diagonal length of which is 36 cm. Find the radius of the base of the cylinder.
The diagonal of the square and two adjacent sides form a right-angled triangle, according to the Pythagorean theorem:
a ^ 2 + a ^ 2 = d ^ 2;
2a ^ 2 = d ^ 2;
a ^ 2 = d ^ 2/2 = 36 ^ 2/2 = 1296/2 = 648;
a = √648 = 18√2 – side of the square.
Since the axial section of the cylinder is a square, the diameter of the base of the cylinder is equal to the side of this square, respectively, the radius of the base is half of this side:
r = a / 2 = 18√2 / 2 = 9√2 ≈ 12.73 cm.
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