Question

match the 2 - dimensional cross - section with the correct 3 - dimensional figure.
right cone: sliced vertically through the apex
sphere: sliced horizontally
right square pyramid: sliced at a slant through the sides
right cylinder: sliced vertically through the bases
isosceles triangle rectangle isosceles trapezoid

Explanation:

Step1: Analyze right cone sliced vertically through apex

When a right cone is sliced vertically through the apex, the cross - section is an isosceles triangle. The two equal sides are the slant heights of the cone, and the base is the diameter of the base of the cone (if we consider the vertical slice).

Step2: Analyze sphere sliced horizontally

A sphere, when sliced at any angle (including horizontally), the cross - section is a circle. This is because a sphere is symmetric in all directions.

Step3: Analyze right square pyramid sliced at a slant through the sides

For a right square pyramid, when sliced at a slant through the sides, the cross - section is an isosceles trapezoid. The non - parallel sides are equal in length.

Step4: Analyze right cylinder sliced vertically through the bases

When a right cylinder is sliced vertically through the bases, the cross - section is a rectangle. The height of the rectangle is the height of the cylinder, and the base of the rectangle is the diameter of the base of the cylinder.

Answer:

• right cone: sliced vertically through the apex $\to$ isosceles triangle
• sphere: sliced horizontally $\to$ circle
• right square pyramid: sliced at a slant through the sides $\to$ isosceles trapezoid
• right cylinder: sliced vertically through the bases $\to$ rectangle