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

Questions

1. 1.

   A composite solid consists of a rectangular prism with dimensions 10 cm by 6 cm by 5 cm surmounted by a right triangular prism whose triangular base has a width of 6 cm, an altitude of 4 cm, and a length of 10 cm. What is the total volume of the composite solid, in cubic centimeters?

   • A) 420
   • B) 480
   • C) 540
   • D) 660
2. 2.

   A solid is formed by attaching one face of a smaller cube with an edge length of 2 cm to the center of one face of a larger cube with an edge length of 5 cm. What is the total surface area of the resulting composite solid?

   • A) 154 square centimeters
   • B) 166 square centimeters
   • C) 170 square centimeters
   • D) 174 square centimeters
3. 3.

   A composite solid is formed by attaching a hemisphere to one circular base of a right circular cylinder with the same radius. If the cylinder has a base radius of 3 centimeters and a height of 8 centimeters, what is the total volume of the composite solid?

   • A) $72\pi$ cubic centimeters
   • B) $81\pi$ cubic centimeters
   • C) $108\pi$ cubic centimeters
   • D) $90\pi$ cubic centimeters
4. 4.

   A composite solid is formed by attaching the base of a right square pyramid to the top square face of a cube with an edge length of 6 cm. If the height of the pyramid is 4 cm, what is the total volume of the composite solid?

   • A) 240 cm³
   • B) 264 cm³
   • C) 288 cm³
   • D) 360 cm³
5. 5.

   A composite solid is formed by attaching the base of a right circular cone to one circular base of a right circular cylinder of the same radius. Given that the base radius is $3\text{ cm}$, the cylinder height is $10\text{ cm}$, and the cone slant height is $5\text{ cm}$, what is the total surface area of the composite solid?

   • A) $75\pi\text{ cm}^2$
   • B) $93\pi\text{ cm}^2$
   • C) $84\pi\text{ cm}^2$
   • D) $102\pi\text{ cm}^2$