Question

which two - dimensional shape, when rotated around its axis, would result in the three - dimensional shape shown?

an isosceles triangle rotated vertically about its base
a rectangle rotated vertically about one of its longer sides
a right triangle rotated horizontally about its hypotenuse
a circle rotated vertically about its diameter

Explanation:

Step1: Analyze the first option

An isosceles triangle rotated vertically about its base forms a double - cone shape.

Step2: Analyze the second option

A rectangle rotated vertically about one of its longer sides forms a cylinder.

Step3: Analyze the third option

A right triangle rotated horizontally about its hypotenuse forms a shape that is not the given three - dimensional shape.

Step4: Analyze the fourth option

A circle rotated vertically about its diameter forms a sphere.

Answer:

None of the options provided are correct. If we assume the three - dimensional shape is a sphere (the most common shape related to rotation of a circular - based 2D shape), the correct 2D shape is a circle rotated about its diameter. But if we consider the general concept of rotation:

• For an isosceles triangle rotated about its base: double - cone.
• For a rectangle rotated about a longer side: cylinder.
• For a right - triangle rotated about hypotenuse: complex non - standard 3D shape.
• For a circle rotated about diameter: sphere.

If the three - dimensional shape in the image is a sphere (assuming the purple shape is a hemisphere, and full rotation of a circle about its diameter gives a sphere), the answer is “a circle rotated vertically about its diameter”.