Question

6.The total surface area of a cube is 96cm².The volume of the cube is

(a)8cm³

(b)512cm³

(c)64cm³

(d)27cm³​

Answer 1

Answer:

(c) Surface area of a cube = 96 cm2

Surface area of a cube = 6 (Side)2 = 96 ⇒ (Side)2 = 16

⇒ (Side) = 4 cm

[taking positive square root because side is always a positive quantity]

Volume of cube = (Side)3 = (4)3 = 64 cm3

Hence, the volume of the cube is 64 cm3.

Answer 2

$\purple{ \boxed{\boxed{\sf{\large{ \red{ (C) = Volume = 64 \: {cm}^{3} }}}}}}$

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Given :-

• Cube
• Total surface area = 96 cm².

To find :-

• Volume of cube

Solution :-

We know that Formula for finding the Total Surface Area of cube is

${\boxed{\sf{Total \: Surface \: Area _ {(cube)}= 6 {a}^{2} }}}$

Were as

• a denotes for side of cube.

● Substituting the given values in formula for finding side of square :-

${ \implies{\sf{Total \: Surface \: Area _ {(cube)}= 6 {a}^{2} }}} \\ \\ { \implies{\sf{96= 6 {a}^{2} }}} \\ \\ { \implies{\sf{ \cfrac{96}{6} = {a}^{2} }}} \\ \\ { \implies{\sf{16= {a}^{2} }}} \\ \\ { \implies{\sf{a = \sqrt{16} }}} \\ \\ { \underline{ \boxed{ \purple{ \implies{\sf{a = 4 \: cm}}}}}}$

So, Length of side of cube is 4 cm.

_____________________________________

Also, Formula for finding Volume of cube is :-

${\boxed{\sf{Volume_{(Cube)} = a^{3}}}}$

Whereas,

• a denotes length of side of cube .

●So, Volume of the Cube is :-

${\large{ \implies{\sf{Volume_{(Cube)} = a^{3}}}}} \\ \\ { \large{ \implies{\sf{Volume_{(Cube)} = (4)^{3}}}}} \\ \\ { \underline{ \boxed{ \red{ \large{ \implies{\sf{Volume_{(Cube)} = 64 \: {cm}^{3} }}}}}}}$

Hence option c is correct.