Question

9. The surface area of each face of a cube is (x2 + 4x + 4) cm. Find (i) the length (ii) the volume of the cube. ​

Answer 1

Answer:

(I) 12 cm

(ii) 23 cm

Step-by-step explanation:

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Answer 2

(i) The length of the cube = ( x + 2 ) cm

(ii) The volume of the cube = ( x³ + 6x² + 12x + 8 ) cm³

Given :

The surface area of each face of a cube is ( x² + 4x + 4 ) cm

To find :

(i) The length of the cube

(ii) The volume of the cube

Solution :

Step 1 of 2 :

Find side of the cube

Let side of the cube = a cm

The surface area of each face = a² cm²

By the given condition

$\displaystyle \sf{ \implies {a}^{2} = {x}^{2} + 4x + 4 }$

$\displaystyle \sf{ \implies {a}^{2} = {(x + 2)}^{2} }$

$\displaystyle \sf{ \implies a = x + 2 }$

Side of the cube = x + 2 cm

Step 2 of 2 :

Find volume of the cube

The volume of the cube

$\sf = {a}^{3} \: \: \: {cm}^{3}$

$\sf = {(x + 2)}^{3} \: \: \: {cm}^{3}$

$\sf = ( {x}^{3} + 3. {x}^{2}.2 + 3.x. {2}^{2} + {2}^{3} ) \: \: \: {cm}^{3}$

$\sf = ( {x}^{3} + 6{x}^{2}+ 12x + 8 ) \: \: \: {cm}^{3}$

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