Question

Math

Posted 2 months ago

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Consider the following figure:
What solid 3D object is produced by rotating the rectangle about line $m$ ?
Choose 1 answer:
(A) A cylinder with diameter 8 units
(B) A cylinder with radius 1 unit
(C) A cone with radius 8 units
(D) A cone with diameter 1 units
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Answer from Sia

Posted 2 months ago

Solution by Steps

step 2

The rectangle has a length of 4 units and a width of 1 unit. When rotating the rectangle about line $m$, the width becomes the radius of the resulting 3D object

step 3

Since the width is 1 unit, the resulting 3D object will have a radius of 1 unit

step 4

The length of the rectangle does not affect the radius of the 3D object but determines the height of the cylinder

step 5

Therefore, the 3D object formed is a cylinder with a radius of 1 unit, not a cone, and the diameter is twice the radius, which would be 2 units, not 8 units

1 Answer

B

Key Concept

3D object formation by rotation

Explanation

When a 2D shape is rotated about a line, the distance from the line to the farthest point on the shape becomes the radius of the resulting 3D object. In this case, rotating a rectangle about a line parallel to its width forms a cylinder with the width as its radius.

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