Grade 8 Volume: Composite Solids

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   An L-shaped step is made of two rectangular prisms. One is 8 in by 7 in by 6 in. The other is 6 in by 7 in by 6 in. What is the total volume in cubic inches?

   1. First prism: 8 × 7 × 6 = 336.
   2. Second prism: 6 × 7 × 6 = 252.
   3. 336 + 252 = 588. The total volume is 588 cubic inches.

   Answer: 588

2. Example 2

   A grain silo is a cylinder with radius 3 in and height 17 in, topped with a hemisphere (half sphere) of radius 3 in. What is the silo's total volume in cubic inches? Use π ≈ 3.14.

   1. Find each part, then add.
   2. Cylinder: 3.14 × 9 × 17 = 3.14 × 153 = 480.42.
   3. Half sphere: ½ × ⁴⁄₃ × π × r³ = ⅔ × 3.14 × 27 = 3.14 × 18 = 56.52.
   4. 480.42 + 56.52 = 536.94. The volume is 536.94 cubic inches.

   Answer: 536.94

3. Example 3

   A cone with radius 4 in and height 9 in is carved out of a cylinder with the same radius and height. What volume is left, in cubic inches? Use π ≈ 3.14.

   1. Cylinder: 3.14 × 16 × 9 = 3.14 × 144 = 452.16.
   2. The cone is ⅓ of that: 452.16 ÷ 3 = 150.72.
   3. 452.16 − 150.72 = 301.44. The volume left is 301.44 cubic inches.

   Answer: 301.44