Question

rotate each shape about the line and find the matching solid.

Explanation:

Analyze the first shape and axis of rotation

$$ \text{Shape: Square of side length } s. $$

$$ \text{Axis of rotation: Along one of the vertical edges of the square.} $$

$$ \text{Resulting solid: A solid cylinder of radius } s \text{ and height } s \text{ (Solid A).} $$

Analyze the second shape and axis of rotation

$$ \text{Shape: Square of side length } s. $$

$$ \text{Axis of rotation: Vertical line of symmetry passing through the center of the square.} $$

$$ \text{Resulting solid: A solid cylinder of radius } \frac{s}{2} \text{ and height } s \text{ (Solid B).} $$

Analyze the third shape and axis of rotation

$$ \text{Shape: Square of side length } s. $$

$$ \text{Axis of rotation: Diagonal line passing through two opposite vertices.} $$

$$ \text{Resulting solid: Two congruent cones joined at their bases (Solid C).} $$

Answer:

Question 1

The square rotated about its outer vertical edge matches:
<blank>A</blank>

Question 2

The square rotated about its central vertical axis of symmetry matches:
<blank>B</blank>

Question 3

The square rotated about its diagonal axis matches:
<blank>C</blank>