Volume of cylinders, cones, spheres Knowledge-Based Download PDF

Questions

1. 1.

   A right circular cone has a height of 12 cm and a slant height of 13 cm. What is the volume of the cone, in cubic centimeters?

   • A) $65\pi$
   • B) $100\pi$
   • C) $130\pi$
   • D) $300\pi$
2. 2.

   A sphere with a radius of 6 cm is tightly inscribed inside a right circular cylinder such that it touches the top base, the bottom base, and the lateral surface of the cylinder. What is the volume of the space inside the cylinder that is outside the sphere, in cubic centimeters?

   • A) $72\pi$
   • B) $108\pi$
   • C) $144\pi$
   • D) $216\pi$
3. 3.

   A solid sphere with a radius of 3 cm is completely submerged in a vertical right circular cylinder with a base radius of 4 cm that contains water. Assuming no water overflows, by how many centimeters does the water level rise?

   • A) 2.25 cm
   • B) 1.50 cm
   • C) 2.75 cm
   • D) 3.00 cm
4. 4.

   A solid metal sphere with a radius of 6 cm is melted and completely recast into a solid right circular cone with a base radius of 6 cm. What is the height of the cone, in centimeters?

   • A) 8 cm
   • B) 12 cm
   • C) 18 cm
   • D) 24 cm
5. 5.

   A solid cylinder, a solid cone, and a solid sphere each have a radius of 3 cm. If the cylinder has a height of 8 cm and the cone has a height of 12 cm, what is the total combined volume of the three solids, in cubic centimeters?

   • A) $144\pi$
   • B) $216\pi$
   • C) $126\pi$
   • D) $120\pi$