a cylinder and a cube are shown.
statements are given about the shape of the cross - section that would result from slicing the figures in different ways.
determine whether each statement about the resulting cross - section matches one or both of the figures shown.
the cross - section for a slice parallel to the base would be congruent to the base.
the cross - section for a slice perpendicular to the base would be the same shape as the base.
the cross - section for a slice parallel or perpendicular to the base could result in a shape with 4 sides.

Question

Accepted Answer

# Explanation:
## Step1: Analyze the first statement for Cylinder and Cube
- For Cylinder: The base of a cylinder is a circle. A slice parallel to the base will also be a circle, congruent to the base. So Cylinder: True.
- For Cube: The base of a cube is a square. A slice parallel to the base will be a square, congruent to the base. So Cube: True.

## Step2: Analyze the second statement for Cylinder and Cube
- For Cylinder: The base is a circle. A slice perpendicular to the base (along the height) will be a rectangle (or square if diameter = height), not a circle. So Cylinder: False.
- For Cube: The base is a square. A slice perpendicular to the base (along the edge) will be a square, same as the base. So Cube: True.

## Step3: Analyze the third statement for Cylinder and Cube
- For Cylinder: A slice parallel to the base is a circle (3 - sided? No, circle is a curve, but in terms of sides, a circle has no straight sides. A slice perpendicular to the base is a rectangle (4 - sided). So for Cylinder, a perpendicular slice gives a 4 - sided shape. So Cylinder: True (perpendicular slice gives 4 - sided).
- For Cube: A slice parallel (square, 4 - sided) or perpendicular (square, 4 - sided) to the base will result in a 4 - sided shape. So Cube: True.

# Answer:
| Statement | Cylinder | Cube |
|--|--|--|
| The cross - section for a slice parallel to the base would be congruent to the base. | $\boxed{True}$ | $\boxed{True}$ |
| The cross - section for a slice perpendicular to the base would be the same shape as the base. | $\boxed{False}$ | $\boxed{True}$ |
| The cross - section for a slice parallel or perpendicular to the base could result in a shape with 4 sides. | $\boxed{True}$ (perpendicular slice) | $\boxed{True}$ |

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QUESTION IMAGE

Question

Explanation:

Step1: Analyze the first statement for Cylinder and Cube

Step2: Analyze the second statement for Cylinder and Cube

Step3: Analyze the third statement for Cylinder and Cube

Answer:

Statement	Cylinder	Cube
The cross - section for a slice perpendicular to the base would be the same shape as the base.	$\boxed{False}$	$\boxed{True}$
The cross - section for a slice parallel or perpendicular to the base could result in a shape with 4 sides.	$\boxed{True}$ (perpendicular slice)	$\boxed{True}$