Question

The total surface area of a cube is 96 sq. cm. The volume of the cube is :

8 cubic cm
512 cubic cm
64 cubic cm
27 cubic cm​

Answer 1

Answer:

64

cubic

cm

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Answer 2

64 cm cube

Given :-

• Total surface area of cube is 96 cm²

To find :- Volume of cube

Concept:-

• First we have to find edge of cube for Volume of cube by using Total surface area of cube.

$\large\bf\underline\blue{SolutioN}$

Formula for Total surface area of cube:

$\large\red{\underline{{\boxed{\textbf{<strong>T</strong><strong>.</strong><strong>S</strong><strong>.</strong><strong>A</strong><strong> </strong>\:of \:cube\: =\: 6a²}}}}}$

In which T.S.A is Total surface area and 'a' is edge of cube

Now , Substitute T.S.A in above formula

→ 96 = 6a²

→ 96/6 = a²

→ 16 = a²

→ √16 = a

→ 4cm = a

So, edge of cube is 4cm.

Formula for Volume of cube :-

$\large\red{\underline{{\boxed{\textbf{Volume\:of \:cube\: =\:a³ }}}}}$

→ Volume of cube = (4)³

→ Volume of cube=64 cm³

Hence required volume of cube is 64 cm³