The diagonal of the axial section of the cylinder is 12 and makes an angle of 450 with the plane of the base of the cylinder. Find the area of the axial section.
Let’s draw a cylinder, the axial section of the cylinder passes through the diameter of the base, we will designate it ABCD, this is a rectangle.
Its diagonal CB, forms with the base plane (base diagonal), angle <BCD = 45`.
Consider a triangle BCD, <C = 45`, <D = 90`, find the angle <B:
<B = 180-90-45 = 45`, so the triangle BCD is isosceles, with the base CB. This means that the sides CD and BD are equal.
Now consider the rectangle ABCD, CD and BD are equal, which means it is a square.
Let’s find the area of the square ABCD, through the diagonal:
S = (d ^ 2) / 2 = (12 ^ 2) / 2 = 72 cm ^ 2
Answer: cross-sectional area 72 cm ^ 2
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