Question

Calculate the difference between the volume of a two cuboidal box whose dimensions are 7x × 3x³ × 5x⁵ and 5x × 3x² × 2x⁶ respectively.
1. 85x⁹
2. 75x⁸
3. 75x⁹
4. 85x⁸

Answer 1

Correct Answer - Option 3 : 75x⁹

Given:

Dimensions of cuboid 1

Length = 7x

Breadth = 3x³

Height = 5x5

​Dimensions of cuboid 2

Length = 5x

Breadth = 3x2

Height = 2x6

Formula used:

Volume of cuboid = Length × Breadth × Height

Using exponents rule: xa × xb = x(a + b)

Calculation:

Dimensions of cuboid 1:

7x × 3x3 × 5x5

Multiply 7, 3, and 5

= 105 × x × x³ × x5

Using exponents rule: xa × xb = x(a+b)

105x1+3+5 = 105x⁹

Dimensions of cuboid 2:

5x × 3x2 × 2x6

Multiply 5, 3 and 2

30 × x × x² × x⁶ = 30x⁹

∴ Difference between the dimension of cuboid = 105x⁹ - 30x⁹ 

∴ Difference between the dimension of cuboidal box = 75x⁹