Question

Which of the following is a three-dimensional figure formed by rotating a two-dimensional figure around the y-axis? Select all that apply. (MORE THAN ONE)

prism

cylinder

circle

cone

sphere

Answer 1

Answer with explanation:

2)

Cylinder.

A cylinder is formed on rotating a rectangle around y-axis.

4)

Cone-

A cone is formed on rotating a two-dimensional figure ( triangle) around the y-axis.

5)

Sphere-

A sphere is formed on rotating a semicircle ( which is a two dimensional figure) around y-axis.

• We will never get a circle since it is not a 3-dimensional figure it is a 2-dimensional figure.

• Similarly we will never get a prism since on rotating around y-axis we will always get a curved figure ( such as cone, cylinder etc) but prism is a plane figure.

Answer 2

The only given three-dimensional figures formed by rotating a two-dimensional figure around the y-axis are; Cylinder, Cone , Sphere

Translation by Rotation

A three dimensional figure is defined as one that has a length, width and height.

Let us look at each of the given options;

1) Prism; This is a not formed by rotating a two-dimensional figure around the y-axis because of the presence of both a rectangle and a triangle face.

2) Cylinder; Yes this is a three dimensional figure formed by rotating a rectangle which is a two-dimensional figure around the y-axis.

3) Circle; This is a two dimensional figure

4) Cone; Yes this is a three dimensional figure formed by rotating a triangle which is a two-dimensional figure around the y-axis.

5) Sphere; Yes this is a three dimensional figure formed by rotating a semi circle which is a two-dimensional figure around the y-axis.

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