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QuestionMathematics

Give some examples of real-life objects that are solids of revolution.
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Step 1:
: A solid of revolution is a three-dimensional shape formed by rotating a two-dimensional shape around an axis.

In real life, there are several examples of solids of revolution.

Step 2:
: One common example is a cylinder, which is formed by rotating a rectangle around an axis parallel to one of its sides.

For instance, a tin can or a water bottle can be considered as solids of revolution. \text{Cylinder formula:} \quad V = \pi r^2 h

Step 3:
: Another example is a cone, which is formed by rotating a right triangle with one vertex at the origin and the hypotenuse lying along the positive x-axis around the y-axis.

An ice cream cone is a real-life example of a cone, which is a solid of revolution.

Step 4:
: A sphere is also a solid of revolution, formed by rotating a semicircle around its diameter.

A soccer ball or a marble are examples of spheres in real life.

Step 5:
: A torus, or a doughnut shape, is formed by rotating a circle around an axis that does not intersect the circle.

A real-life example is a tire or a lifebuoy ring. \text{Torus formula:} \quad V = 2 \pi^2 R r^2 where R is the distance from the center of rotation to the center of the circle, and r is the radius of the circle.

Final Answer

Real-life objects that are solids of revolution include cylinders (tin cans, water bottles), cones (ice cream cones), spheres (soccer balls, marbles), and tori (tires, lifebuoy rings).