Find the volume of the cuboid whose dimensions are (x + 2),(x – 1) and (x – 3)

Open in App

Solution

Given the dimensions of the cuboid as (x + 2), (x – 1) and (x – 3)

$∴$ Volume of the cuboid = (l × b × h) $u n i t s^{3}$

= (x + 2) (x – 1) (x – 3) $u n i t s^{3}$

We have $(x + a) (x + b) (x + c) = x 3 + (a + b + c) x^{2} + (a b + b c + c a) x + a b c$

$∴$ $(x + 2) (x - 1) (x - 3) = x^{3} + (2 - 1 - 3) x^{2} + (2 (- 1) + (- 1) (- 3) + (- 3) (2)) x + (2) (- 1) (- 3)$

$= x^{3} - 2 x^{2} + (- 2 + 3 - 6) x + 6$

$V o l u m e = x^{3} - 2 x^{3} - 5 x + 6 u n i t s^{3}$

Suggest Corrections

Similar questions

Find the volume of the cuboid whose dimensions are $(x + 2), (x - 1)$ and $(x - 3) .$

(x^{2} - 2), (2 x + 4)

(x - 3) .

(x - 1), (x - 2)

(x - 3)

What are the possible expresssions for the dimensions of the cuboid whose volume is $3 x^{2} - 12 x$ ?

Join BYJU'S Learning Program