GCSE Maths Hard Question Help!?

Question

The base of a cuboid is a square of side x cm
The height of the cunoid is 9x+4) cm
The volume of the cuboid is 100cm3

Find the height

Answer 1

Given that,

The base of a cuboid is a square of side x cm

The height of the cunoid = h = (9x+4) cm

The volume of the cuboid = V = 100cm3

=> lbh = 100

=>  x*x*(9x+4) = 100

=> 9x^3 + 4x^2 = 100

=> 9x^3 + 4x^2 - 100 = 0

By using graph of y = 9x^3 + 4x^2 - 100 we will get x = 2.0927 cm.

Substitute x = 2.0927 cm in h = (9x + 4) cm we get,

                                            h = 2.0927*9+4

                                               =22.83 cm

Therefore height of the cuboid = 22.83 cm

Answer 2

The base of a cuboid is a square of side x cm.

The height of the cuboid = h = (9x+4) cm.

The volume of the cuboid = V = 100cm3.

=> lbh = 100

=>  x*x*(9x+4) = 100

=> 9x³ + 4x² = 100

=> 9x³ + 4x² - 100 = 0.

To draw the graph by using table values as shown below.

To make the table, choose the value for x and substitute in the original equation and obtain random values for y.

 

x	y = 9x3 + 4x2 - 100	(x, y)
- 2	y = 9(- 2)3 + 4(- 2)2 - 100 = - 72 + 16 -100 = - 156	(- 2, - 156)
- 1	y = 9(- 1)3 + 4(- 1)2 - 100 = - 9 + 4 -100 = - 105	(- 1, - 105)
0	y = 9(0)3 + 4(0)2 - 100 = 0 + 0 -100 = - 100	(0, - 100)
1	y = 9(1)3 + 4(1)2 - 100 = 9 + 4 -100 = - 87	(1, - 87)
2	y = 9(2)3 + 4(2)2 - 100 = 72 + 1 -100 = - 27	(2, - 27)
2.5	y = 9(2.5)3 + 4(2.5)2 - 100 = 140.625 + 25 -100 = 65.625	(2.5, 65.625)

By using graph of y = 9x^3 + 4x^2 - 100 we will get x = 2.0927 cm.

Substitute x = 2.0927 cm in h = (9x + 4) cm we get,

                                            h = 2.0927*9+4

                                               =22.83 cm

Therefore height of the cuboid = 22.83 cm.