Question

US_

Diagram NOT
accurately draw
(x + 1)cm
(3 - x) cm
(2x + 5) cm
The diagram shows a cuboid of volume V cm3
(a) Show that V = 15 + 16x - x (squared) - 2x (cubed)

Answer 1

Explanation:

Length of the cuboid = ((2x + 5) cm

Width of the cuboid = (3 - x) cm

Height of the cuboid = (2x + 5) cm

Since, volume of the cuboid = Length × Width × Height

= (2x + 5)(3 - x)(x + 1)

= [2x(3 - x) + 5(3 - x)](x + 1)

= (6x - 2x² + 15 - 5x)(x + 1)

= (-2x² + x + 15)(x + 1)

= x(-2x² + x + 15) + 1(-2x² + x + 15)

= -2x³ + x² + 15x - 2x² + x + 15

= -2x³ - x² + 16x + 15

≈ 15 + 16x - x² - 2x³