Question

A rectangular box of width(a), length(b), and height(c) has a solid cylinder of height 'c' and of diameter 'a' placed within it. If a= 6, b =8 and c =10, how much volume is left in the rectangular box ?
1. 480 − 180π
2. 240 − 96π
3. 380 − 90π
4. 480 − 90π

Answer 1

Correct Answer - Option 4 : 480 − 90π

Calculation:

The volume of the rectangular box left = volume of the rectangular box - the volume of the cylinder inside it

Volume of rectangular box = a × b × c = 6 × 8 × 10

Volume of rectangular box = 480 cubic units

Volume of cylinder = π × (a/2)² × c = 10 × (6/2)² × π

Volume of cylinder = 90π  cubic units

Left out volume = 480 - 90π 

∴ The remaining volume is 480 - 90π.