Question

If the edge of a cube is increased by 4 cm, its volume increases to 988 cm3 What is the actual edge length of each edge of the cube?​

Answer 1

Given :

If the edge of a cube is increased by 4 cm, its volume increases to 988 cm3 What is the actual edge length of each edge of the cube?

To Find :

What is the actual edge length of each edge of the cube?

Solution :

Let the edge of cube be a

according to the given condition

Volume of cube + 988 = (edge+4)³

=> a³ + 988 = (a+4)³

Applying identity (a+b)³=a³+b³+3ab(a+b)

=> a³ + 988 = a³ + 64 + 3×a×4(a+4)

=> 988 - 64 = 12a(a+4)

=> 924 = 12a² + 48a

=> 12a² + 48a - 924 = 0

Take 12 as a common

=> 12( a² + 4a - 77) = 0

=> a² + 4a - 77 = 0

Splitting middle term

=> a² + 11a - 7a -77 = 0

=> a(a+11) -7(a+11) = 0

=> (a+11)(a-7) = 0

Either

=> a +11 = 0

=> a = -11

or

=> a - 7 = 0

=> a = 7

Length never in negative

Neglect a = -11

${\boxed{\bf{Actual\:edge\:length\:of\:cube\:=7cm}}}$

Some Identities

• (a+b)² = a²+b²+2ab
• (a-b)² = a²+b²-2ab
• (a-b)³ = a³-b³-3ab(a-b)
• (a+b)³ = a³+b³+3ab(a+b)
• a²-b² = (a+b)(a-b)
• a³+b³ = (a+b)(a²-ab+b²)
• a³-b³ = (a-b)(a²+ab+b²)

Answer 2

✬ Edge = 7 Cm ✬

Step-by-step explanation:

Given:

• Edge of a cube is increased by 2 cm.
• Then, it's volume is also increases to 988 cm³.

To Find:

• What is the actual length of each edge of the cube?

Solution: Let the edge of original cube was x cm.

∴ Volume of original cube = (edge)³ = x³

• After increasing its edge by 4 cm •

• New edge = (x + 4)³

A/q

$\small\implies{\sf }$ (x + 4)³ = x³ + 988

$\small\implies{\sf }$ x³ + 4³ + 3(x)(4) (x + 4) = x³ + 988 [ (a + b)³ = a³ + b³ + 3ab (a + b) ]

$\small\implies{\sf }$ x³ + 64 + 12x (x + 4) = x³ + 988

$\small\implies{\sf }$ x³ + 64 + 12x² + 48x = x³ + 988

$\small\implies{\sf }$ x³ + 12x² + 48x = x³ + 988 – 64

$\small\implies{\sf }$ 12x² + 48x = 924

$\small\implies{\sf }$ 12x² + 48x – 924 = 0

$\small\implies{\sf }$ 12 (x² + 4x – 77) = 0

$\small\implies{\sf }$ 12 (x² +11x – 7x – 77) = 0

$\small\implies{\sf }$ x² + 11x – 7x – 77 = 0/12

$\small\implies{\sf }$ x (x + 11) –7 (x + 11) = 0 [ By middle term splitting ]

$\small\implies{\sf }$ (x – 7) (x + 11)

Hence, x – 7 = 0 or x = 7

and x + 11 = 0 or x = –11 ( This is not possible )

∴ Length of eshe of original cube was x = 7cm and it's volume = (7)³ = 343