Area, volume and surface area of composite figures Knowledge-Based Practice

Questions

1. 1.

   A solid block is formed by drilling a cylindrical hole of radius 3 cm completely through the center of a right rectangular prism with a square base of side length 10 cm and a height of 8 cm. What is the volume of the remaining composite solid, in cubic centimeters?

   • A) $800 - 72\pi$
   • B) $800 - 24\pi$
   • C) $800 - 144\pi$
   • D) $800 - 36\pi$
2. 2.

   A solid toy consists of a right circular cone joined base-to-base to a hemisphere of radius 4 cm. If the total height of the toy is 11 cm, what is the total volume of the composite solid?

   • A) $64\pi\text{ cm}^3$
   • B) $72\pi\text{ cm}^3$
   • C) $96\pi\text{ cm}^3$
   • D) $80\pi\text{ cm}^3$
3. 3.

   A solid figure is formed by attaching a hemisphere onto one flat circular base of a right circular cylinder of the same radius. If the cylinder has a radius of 3 cm and a height of 8 cm, what is the total surface area of the composite solid?

   • A) $66\pi\text{ cm}^2$
   • B) $75\pi\text{ cm}^2$
   • C) $84\pi\text{ cm}^2$
   • D) $93\pi\text{ cm}^2$
4. 4.

   A solid composite figure is composed of a right circular cylinder with a base radius of 3 cm and a height of 10 cm, surmounted by a right circular cone with the same base radius and a height of 4 cm. What is the total volume of this composite solid?

   • A) $102\pi\text{ cm}^3$
   • B) $126\pi\text{ cm}^3$
   • C) $94\pi\text{ cm}^3$
   • D) $138\pi\text{ cm}^3$
5. 5.

   A solid composite figure is formed by attaching the base of a right square pyramid directly onto one face of a cube with edge length 6 cm. If the slant height of each triangular face of the pyramid is 5 cm, what is the total surface area of the composite solid?

   • A) 312 cm²
   • B) 276 cm²
   • C) 204 cm²
   • D) 240 cm²

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