Question

the diagonal of cube is 16 root 3 cm find its surface area and volume​

Answer 1

${\bold{\underline{\underline{Answer:}}}}$

${\bold{\therefore T.S.A\:of\:cube=1536\:cm^{2}}}$

${\bold{\therefore Volume\:of\:cube=4096\:cm^{3}}}$

${\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\underline \bold{Given : } \\ \implies Diagonal = 16 \sqrt{3} \: cm \\ \\ \underline \bold{To \: Find : } \\ \implies T.S.A\: of \: cube = ? \\ \\ \implies Volume \: of \: cube = ?$

• According to given question :

$\bold{Using \: formula \: of \: Diagonal \: of \: cube : } \\ \implies Diagonal \: of \: cube = 16 \sqrt{ 3} \\ \\ \implies \sqrt{3} a = 16 \sqrt{3} \\ \\ \implies a = \frac{16 \cancel{\sqrt{3}} }{ \cancel{\sqrt{3}} } \\ \\ \bold{\implies a = 16 \: cm} \\ \\ \bold{For \: T.S.A \: of \: cube : } \\ \implies T.S.A \: of \: cube = 6 {a}^{2} \\ \\ \implies T.S.A= 6 \times 16 \times 16 \\ \\ \implies T.S.A= 6 \times 256 \\ \\ \bold{\implies T.S.A= 1536 \: cm^{2} } \\ \\ \bold{For \: Volume : } \\ \implies Volume \: of \: cube = {a}^{3} \\ \\ \implies Volume = 16 \times 16 \times 16 \\ \\ \bold{\implies Volume = 4096 \: cm^{3} }$

Answer 2

$\bold{using \: formula \: of \: diagonal \: of \: cube : } \\ \implies diagonal \: of \: cube = 16 \sqrt{ 3} \\ \\ \implies \sqrt{3} a = 16 \sqrt{3} \\ \\ \implies a = \frac{16 \cancel{\sqrt{3}} }{ \cancel{\sqrt{3}} } \\ \\ \bold{\implies a = 16 \: cm} \\ \\ \bold{for \: t.s.a \: of \: cube : } \\ \implies t.s.a \: of \: cube = 6 {a}^{2} \\ \\ \implies t.s.a = 6 \times 16 \times 16 \\ \\ \implies t.s.a = 6 \times 256 \\ \\ \bold{\implies t.s.a = 1536 \: cm^{2} } \\ \\ \bold{for \: volume : } \\ \implies volume \: of \: cube = {a}^{3} \\ \\ \implies volume = 16 \times 16 \times 16 \\ \\ \bold{\implies volume = 4096 \: cm^{3} }$