Question

11. Total surface Area of a cube
is 96cm2. The volume of the
cube is
O A) 8 cm
B) 512 cm
O C) 64 cm
O D) 27 cm

Answer 1

★GIVEN★

Total surface Area of a cube is 96 cm2.

★To Find★

The volume of the cube.

★SOLUTION★

We know that,

$\large{\blue{\underline{\boxed{\bf{Surface\:Area\:of\:cube\:=6{a}^{2}}}}}}$

where,

• a is the side.

According to the question,

$\large\implies{\sf{Surface\:Area=6{a}^{2}}}$

$\large\implies{\sf{96=6{a}^{2}}}$

$\large\implies{\sf{\dfrac{96}{6}={a}^{2}}}$

$\large\implies{\sf{\dfrac{\cancel{96}}{\cancel{6}}={a}^{2}}}$

$\large\implies{\sf{16={a}^{2}}}$

Square rooting both the sides,

$\large\implies{\sf{\sqrt{16}=a}}$

$\large\implies{\sf{\frac{+}{-}4=a}}$

$\large\therefore\boxed{\bf{a=\frac{+}{-}4\:cm.}}$

Now,

$\large{\blue{\underline{\boxed{\bf{Volume\:of\:cube\:={a}^{3}}}}}}$

$\large\implies{\sf{Volume={a}^{3}}}$

$\large\implies{\sf{Volume={(4)}^{3}}}$

$\large\implies{\sf{Volume=64\:{cm}^{3}.}}$

$\large{\blue{\underline{\boxed{\bf{Volume\:of\:cube\:is\:64\:{cm}^{3}.}}}}}$

So your answer is option (C).