Problem Solving

svd.kumar wrote:A rectangular box has the dimensions 12 inches x 10 inches x 8 inches. What is the
largest possible volume of a right cylinder that is placed inside the box?

If a right cylinder is fitted tightly inside a rectangular box, then the right cylinder will have the length equal to the length of one of the sides of the box and it will have a diameter equal to the length of the smallest of rest two sides of the box.

Volume of a right cylinder with height h and radius r is πr²h

Hence, possible combinations for the cylinder in this case

• 1. Height = 12, Diameter = 8 --> Radius = 4 --> Volume = 192Ï€
  2. Height = 10, Diameter = 8 --> Radius = 4 --> Volume = 160Ï€
  3. Height = 8, Diameter = 10 --> Radius = 5 --> Volume = 200Ï€ --> MAXIMUM

The correct answer is A.