Question

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Answer 1

A cylinder is a three-dimensional geometric shape that consists of two parallel, congruent circular bases and a curved surface connecting the bases. It can be visualized as a tube or a can.

Here's a mathematical explanation of key properties and formulas related to a cylinder:

Base: A cylinder has two identical circular bases. The radius of each base is denoted as "r."

Height (or Length): The distance between the two bases is called the height of the cylinder. It is typically denoted as "h."

Lateral Surface: The lateral surface of a cylinder is the curved surface that wraps around the sides of the cylinder. The lateral surface area (A_lateral) can be calculated using the formula:

A_lateral = 2πrh, where "r" is the radius and "h" is the height.

Total Surface Area: The total surface area of a cylinder includes both the lateral surface area and the areas of the two circular bases. It is calculated as:

A_total = 2πrh + 2πr², which can be simplified to:

A_total = 2πr(h + r)

Volume: The volume of a cylinder is the amount of space it encloses. It can be calculated using the formula:

V = πr²h, where "r" is the radius and "h" is the height.

Diameter: The diameter of a cylinder is twice the radius. It is denoted as "d" and is equal to 2r.

Axis: The line segment connecting the centers of the two circular bases is called the axis of the cylinder.

Cross-Section: A cross-section of a cylinder is a two-dimensional shape formed when the cylinder is sliced perpendicular to its axis. It can be a circle, an ellipse, or another shape, depending on the angle and position of the cut.

Cylinders are commonly encountered in everyday life, such as in cans, pipes, and containers. Understanding the properties and formulas associated with cylinders is important in geometry and various applications in engineering, physics, and

Answer 2

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Note: Rotational symmetry refers to the characteristic of a shape or object that remains unchanged when rotated around a fixed point or axis by a certain angle. In other words, if you can rotate an object and it still looks the same in multiple positions, it exhibits rotational symmetry.

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The letter "H" has rotational symmetry. It can be rotated by 180 degrees (half a full rotation) and still look the same.

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Note: When you rotate the letter "H" by 180 degrees, it remains unchanged because the top horizontal bar swaps places with the bottom horizontal bar, resulting in the same appearance. This characteristic indicates that the letter "H" possesses rotational symmetry of order 2.

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Note: A trapezium (also known as a trapezoid in some regions) may or may not have rotational symmetry, depending on its specific shape.

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In summary, an isosceles trapezium has rotational symmetry of order 2, allowing it to be rotated by 180 degrees and still look the same. Other types of trapeziums may not possess rotational symmetry.

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