Cross-sections Knowledge-Based Practice

Questions

1. 1.

   A cube has an edge length of 6 cm. What is the area, in square centimeters, of the cross-section formed by a plane that passes through two diagonally opposite parallel edges of the cube?

   • A) 36
   • B) $36\sqrt{3}$
   • C) 72
   • D) $36\sqrt{2}$
2. 2.

   A right circular cone has a base radius of 8 cm and a slant height of 17 cm. What is the area of the cross-section formed by a plane that passes through the apex of the cone and is perpendicular to its base?

   • A) 60 cm²
   • B) 136 cm²
   • C) 240 cm²
   • D) 120 cm²
3. 3.

   A right circular cylinder has a base radius of 5 cm and a height of 12 cm. What is the area of the cross-section formed by a plane that passes through the centers of both circular bases?

   • A) 60 cm2
   • B) 120 cm2
   • C) 25π cm2
   • D) 120π cm2
4. 4.

   A sphere has a radius of 10 cm. If a plane intersects the sphere at a distance of 6 cm from its center, what is the area of the resulting circular cross-section?

   • A) $16\pi\text{ cm}^2$
   • B) $36\pi\text{ cm}^2$
   • C) $48\pi\text{ cm}^2$
   • D) $64\pi\text{ cm}^2$
5. 5.

   A right square pyramid has a base edge length of 8 units and a height of 6 units. If a plane parallel to the base slices the pyramid at a height of 3 units above the base, what is the area of the resulting cross-section?

   • A) 8 square units
   • B) 12 square units
   • C) 16 square units
   • D) 32 square units

Answers and step-by-step solutions appear after you finish the test.