Question

7. The volume of a cube is 64 cm. Its surface area is​

Answer 1

Step-by-step explanation:

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Answer 2

We have given the volume of a cube which is 64 cm³. So, from that we have to find out its surface area.

For that, first we have to know the side of the cube.

There after , applying formula for finding it's total surface area :

Let's do it :

Formulae need to know -

• ${\boxed{\sf{Volume \: of \: Cube = (Side)^{3}}}}$

• ${\boxed{\sf{Surface \: area \: of \: Cube = 6(Side)^{2}}}}$

• ${\boxed{\sf{Curved \: Surface \: area \: of \: Cube = 4(Side)^{2}}}}$

For Finding Side of the Cube :-

We know,

$:\implies \sf Volume = 64 = (Side)^{3}$

$:\implies \sf Side = 64 \: (Cube \: root)$

$:\implies \sf Side = 4$

$:\implies \sf \underline{ \boxed{\sf Side = 4 \: cm}}$

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Now, Surface Area of Cube :-

$\dashrightarrow\:\:\bf Surface \: area = 6(Side)^{2}$

• Side of Cube → 4 cm

$\dashrightarrow\:\:\sf Surface \: area = 6(4)^{2}$

$\dashrightarrow\:\:\sf Surface \: area = 6 \times 16$

$\dashrightarrow\:\:\sf Surface \: Area = 96$

$\dashrightarrow\:\: \underline{ \boxed{\sf Surface \: area \: of \: Cube = 96 \: cm^{2}}}$

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In the similar way, you can also find out the Curved surface area of it.

$\dashrightarrow\:\:\sf Curved \: Surface \: area = 4(4)^{2}$

$\dashrightarrow\:\:\sf Curved \: Surface \: area = 4 \times 16$

$\dashrightarrow\:\:\sf Curved \: Surface \: Area = 64 \: cm^{2}$

$\dashrightarrow\:\: \underline{ \boxed{\sf Curved \: Surface \: area \: of \: Cube = 64 \: cm^{2}}}$

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Not sure about the answer ?

Let's Verify it !

⠀⠀$\underline{\bf{Verification}}$ ⠀ Eq.(i)

Putting Side = 4 cm

$:\implies \sf Volume = 64 = (Side)^{3}$

$:\implies \sf 64 = (4)^{3}$

$:\implies \sf 64 = 64$

L.HS = R.HS

Hence,

Verified !!

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