Sia
Question
Math
Posted 9 months ago
Consider the following figure:
What solid 3D object is produced by rotating the rectangle about line ?
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 9 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 , 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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