Question

If the volume of a box is 2x3 + 4x2 − 30xwhich of the dimensions are possible with the given x-value?

A. x = 1; dimensions: 8 by 9 by 1
B. x = 1; dimensions: 2 by 5 by 3
C. x = 4; dimensions: 2 by 5 by 3
D. x = 4; dimensions: 8 by 9 by 1

Answer 1

The possible value of x = 4, dimensions 8 by 9 by 1 (option D), if the volume of a box is
`2 x^(3) + 4 x^(2) -30x`.

Explanation:

The given is,

`2 x^(3) + 4 x^(2) -30x`................................(1)

Step:1

Check for option A,

x = 1, dimensions 8 by 9 by 1

From the equation (1),

Volume =
`2 (1^(3)) + 4 (1^(2) )-30(1)`

`=2+4-30` = -24...................(2)

From the dimensions,

Volume = ( 8 × 9 × 1 )

= 72............................................(3)

From equation (2) and (3)

-24 ≠ 72

So, X=1; dimensions 8 by 9 by 1 is not possible.

Check for option B,

x = 1, dimensions 2 by 5 by 3

From the equation (1),

Volume =
`2 (1^(3)) + 4 (1^(2) )-30(1)`

`=2+4-30` = -24...................(4)

From the dimensions,

Volume = ( 2 × 5 × 3 )

= 30.........................................(5)

From equation (4) and (5)

-24 ≠ 30

So, X=1; dimensions 2 by 5 by 3 is not possible.

Check for option C,

x = 4, dimensions 2 by 5 by 3

From the equation (1),

Volume =
`2 (4^(3)) + 4 (4^(2) )-30(4)`

`=2(64)+4(16)-30(4)`

`= 128+64-120`

= 72.............................................(6)

From the dimensions,

Volume = ( 2 × 5 × 3 )

= 30............................................(7)

From equation (6) and (7)

72 ≠ 30

So, X=4; dimensions 2 by 5 by 3 is not possible.

Check for option C,

x = 4, dimensions 8 by 9 by 1

From the equation (1),

Volume =
`2 (4^(3)) + 4 (4^(2) )-30(4)`

`=2(64)+4(16)-30(4)`

`= 128+64-120`

= 72............................................(8)

From the dimensions,

Volume = ( 8 × 9 × 1 )

= 72............................................(9)

From equation (8) and (9)

72 = 72

So, X=4; dimensions 8 by 9 by 3 is possible.

Result:

The possible value of x = 4, dimensions 8 by 9 by 1 (option D), if the volume of a box is
`2 x^(3) + 4 x^(2) -30x`.