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A solid shape is generated by rotating a rectangle about any of its sides. The shape will be :
  • a)
    Cuboid
  • b)
    Cone
  • c)
    Sphere
  • d)
    Cylinder (right circular) 
Correct answer is option 'D'. Can you explain this answer?
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Explanation:

To understand why the correct answer is option 'D' (cylinder), let's break down the process of rotating a rectangle about its sides and examine the resulting shape.

Rotating a Rectangle:

When a rectangle is rotated about one of its sides, the resulting shape is a solid figure with a circular base and two parallel, congruent circular faces on either end. This figure is known as a cylinder.

Properties of a Cylinder:

A cylinder is a three-dimensional solid shape that has the following properties:

1. Bases: The two circular faces at the top and bottom of the cylinder are called bases. These bases are parallel and congruent.

2. Height: The height of the cylinder is the perpendicular distance between the two bases. It represents the distance between the top and bottom faces.

3. Lateral Surface: The curved surface of the cylinder that connects the two bases is called the lateral surface. It is formed by the rectangle being rotated.

4. Axis: The axis of a cylinder is a straight line passing through the center of both bases. It is also the line about which the rectangle was rotated.

5. Volume: The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the radius of the base and h is the height of the cylinder.

6. Surface Area: The surface area of a cylinder can be calculated using the formula A = 2πrh + 2πr^2, where r is the radius of the base and h is the height of the cylinder.

Conclusion:

By rotating a rectangle about any of its sides, we obtain a solid shape known as a cylinder. The cylinder has circular bases, a curved lateral surface, and a straight axis passing through the center of the bases. The volume and surface area of a cylinder can be calculated using specific formulas.
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