12 multiple-choice questions, progressively harder.
What is a plane cross-section of a solid?
Solution
Correct answer: B
A section contains exactly the points shared by the plane and the solid. It has no thickness; a view may instead include points at many depths.
A right box has a 4 cm by 7 cm base and is 9 cm high. An interior plane is parallel to that base. What are the section dimensions?
Correct answer: D
A base-parallel section repeats the base of a prism. Its dimensions are 4 cm by 7 cm; the 9 cm height locates other planes but does not change this section.
An interior plane cuts a pentagonal prism parallel to its bases. What is the section?
Correct answer: A
Parallel sections of a prism are congruent to its base. Five base sides therefore give a congruent pentagonal section.
A right square pyramid is cut parallel to its base strictly between its apex and base. Which section results?
Correct answer: C
The plane crosses all four triangular side faces. Its four sides follow the square base, but lie closer to the apex, giving a smaller square.
A right circular cylinder has radius 6 cm. What is the radius of a section made by an interior plane parallel to its bases?
The cylinder has the same circular section at every interior level parallel to its bases. The section radius is 6 cm.
A right circular cylinder has diameter 8 cm and height 13 cm. What are the dimensions of its section through the axis?
An axial plane crosses each circular end in a diameter. The two upright edges run the full height, making an 8 cm by 13 cm rectangle.
A right circular cone is cut parallel to its base, strictly between the apex and base. What is the true section?
A base-parallel plane cuts the cone at one level. The same radius occurs in every direction about the axis, so the section is circular.
A plane through the axis of a right circular cone cuts the whole solid. What is the true section?
The plane includes the apex and a whole base diameter. Its two sloping sides have equal lengths by the cone's symmetry about the axis.
A plane passes through the interior of a ball but misses its center. What is the section?
All boundary points of the section lie the same distance from its center in the plane. Moving away from the ball center makes this circular disk smaller.
A filled rectangle has sides of 5 cm and 12 cm. It turns fully about a 12 cm side. Which cylinder results?
The fixed side becomes the axis-height, 12 cm. The perpendicular side reaches 5 cm from the axis and sweeps the radius.
A filled right triangle has perpendicular legs of 8 cm and 15 cm. It turns fully about its 8 cm leg. Which solid results?
The fixed 8 cm leg becomes the cone height. The perpendicular 15 cm leg sweeps the circular base radius, while the hypotenuse sweeps the curved side.
A filled semicircular region has radius 4 cm. It turns fully about its diameter. What solid is swept out?
The diameter is the axis, and the arc sweeps the entire sphere boundary. The filled region sweeps the ball inside it; the radius stays 4 cm.
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