3D figures (Cavalieri's principle) Knowledge-Based Download PDF

Questions

1. 1.

   Which of the following conditions guarantees that two three-dimensional solids have equal volumes according to Cavalieri's principle?

   • A) They have equal total surface areas, and all cross sections parallel to their bases have equal perimeters.
   • B) They have equal vertical heights, and all cross sections parallel to their bases have equal areas.
   • C) They have equal vertical heights, and all cross sections parallel to their bases have congruent shapes.
   • D) They have equal base perimeters, and all lateral faces have identical angles of inclination.
2. 2.

   Two solids have the same vertical height, and at every level parallel to their bases, the horizontal cross-sectional area of Solid P is 3 times that of Solid Q. If the volume of Solid Q is 45 cm³, what is the volume of Solid P?

   • A) 15 cm³
   • B) 405 cm³
   • C) 1215 cm³
   • D) 135 cm³
3. 3.

   Two solids have the same vertical height of 12 cm. At every level parallel to their bases, the horizontal cross-sectional area of the first solid equals that of the second solid, which is a pyramid with a rectangular base measuring 10 cm by 12 cm. What is the volume of the first solid?

   • A) 480 cm³
   • B) 1440 cm³
   • C) 720 cm³
   • D) 240 cm³
4. 4.

   Two solids, a cylinder and a triangular prism, have the same height of 20 cm. At every level parallel to their bases, horizontal cross-sections of the two solids have equal areas. If the base of the triangular prism is a right triangle with legs of length 12 cm and 15 cm, what is the volume of the cylinder?

   • A) 1800 cm³
   • B) 3600 cm³
   • C) 600 cm³
   • D) 900 cm³
5. 5.

   A right cylinder and an oblique cylinder have the same height of 15 cm, and every cross-section parallel to their bases has an area of $36\pi$ cm². What is the volume of the oblique cylinder?

   • A) $180\pi$ cm³
   • B) $540\pi$ cm³
   • C) $1080\pi$ cm³
   • D) $270\pi$ cm³