Question

Паралельно осі циліндра,радіус основи дорівнює 4 см,проведено площину. Ця площина перетинає основу циліндра по хорді, що стягує дугу, градусна міра якої дорівнює 60 градусів. Знайдіть площу перерізу циліндра цією площиною, якщо його діагональ дорівнює 8 см.​

Answer 1

Відповідь:

Пояснення: фото

Answer 2

To find the area of the cross-section of the cylinder, we need to determine the length of the chord that intersects the base of the cylinder. We are given that the radius of the base is 4 cm and the diagonal of the cylinder is 8 cm.

Let's break down the problem step by step:

1. Find the length of the chord: - The diagonal of the cylinder is the hypotenuse of a right triangle formed by the radius, the length of the chord, and the perpendicular bisector of the chord. - Using the Pythagorean theorem, we can find the length of the chord. Let's denote the length of the chord as c: - The radius of the base is 4 cm. - The diagonal of the cylinder is 8 cm. - The perpendicular bisector of the chord is half the length of the diagonal, which is 4 cm. - Applying the Pythagorean theorem: c^2 = (2r)^2 - r^2. - Simplifying the equation: c^2 = 16 - 16 = 0. - Therefore, the length of the chord is 0 cm.

2. Calculate the area of the cross-section: - Since the length of the chord is 0 cm, the chord does not intersect the base of the cylinder. - As a result, the cross-section of the cylinder formed by this plane is a circle with a radius of 4 cm. - The formula for the area of a circle is A = πr^2. - Substituting the radius, we get: A = π(4^2) = 16π.

Therefore, the area of the cross-section of the cylinder formed by the given plane is 16π square centimeters.

Please let me know if you need any further clarification or assistance!