Question

If the entire surface area of a cube is 96m', what is its volume ?
(a) 32 m2
(b) 64 m3 (c) 216 m
(d) 125 m​

Answer 1

$\huge\underline\bold\pink{Solution:-}$

Let 'x' be the edge of a cube.

Surface Area of Cube is 6$(x)^2)$

The Surface Area of Cube is Given as 96$cm^2$

96 = 6$(x)^2)$

$(x)^2)$ = 16

$\therefore$ x = 4 cm

Volume of Cube = $(x)^3$ = 64 $cm^3$.

Answer 2

Answer:

${\large{\sf{\pmb{\underline{\green{Given:-}}}}}}$

• ● The entire surface area of a cube is 96m².

${\large{\sf{\pmb{\underline{\green{To \: Find:-}}}}}}$

• ● What is its volume ?

${\large{\sf{\pmb{\underline{\green{Using \: Formulae :-}}}}}}$

$\bigstar{\underline{\boxed{\sf{Surface \: area \: of \:cube=6{\big(a\big)}^{2}}}}}$

$\bigstar{\underline{\boxed{\sf{Volume \: of \: Cube={\big(a\big)}^{3}}}}}$

${\large{\sf{\pmb{\underline{\green{Solution:-}}}}}}$

$\dag \:{\underline{\pmb{\frak{\red{Finding \: the \: side \: of \: cube}}}}}$

${: \implies{\sf{Surface \: area \: of \:cube=\bf{6{\big(a\big)}^{2}}}}}$

• Substituting the values

${: \implies{\sf{96=\bf{6{\big(a\big)}^{2}}}}}$

${: \implies{\sf{\dfrac{96}{6} =\bf{{\big(a\big)}^{2}}}}}$

${:\implies{\sf{\cancel{\dfrac{96}{6}} =\bf{{\big(a\big)}^{2}}}}}$

${:\implies{\sf{16 =\bf{{\big(a\big)}^{2}}}}}$

${:\implies{\sf{ \sqrt{16} =\bf{a}}}}$

${:\implies{\sf{ a =\bf{4}}}}$

${\dag{\underline{\boxed{\sf\pink{\pmb{ Side \: of \: cube ={4}}}}}}}$

• ● Hence, The side of cube is 4 m.

$\dag \: {\underline{\pmb{\frak{\red{Finding \: the \: volume\: of \: cube}}}}}$

${: \implies{\sf{Volume \: of \: Cube= \bf{\big(a\big)}^{3}}}}$

• Substituting the values

${: \implies{\sf{Volume \: of \: Cube= \bf{\big(4\big)}^{3}}}}$

${: \implies{\sf{Volume \: of \: Cube= \bf{4 \times 4 \times 4}}}}$

${: \implies{\sf{Volume \: of \: Cube= \bf{64 \: {m}^{3} }}}}$

${\dag\underline{\boxed{\sf{\pink{\pmb{Volume \: of \: Cube={64 \: {m}^{3}}}}}}}}$

• ● Hence, The volume of Cube is 64 m³.
• ● Henceforth,The option (b) 64³ is the correct answer.

${\large{\sf{\pmb{\underline{\green{Learn \: More :-}}}}}}$

$\begin{gathered}\small\begin{gathered}\bigstar \: \bf\underline{More \: Useful \: Formulae } \: \bigstar  \\ \begin{gathered}{\boxed{\begin{array} {cccc}{\sf{{\leadsto TSA \: of \: cube \: = \: 6(side)^{2}}}} \\  \\ {\sf{{\leadsto LSA \: of \: cube \:= \: 4(side)^{2}}}}  \\  \\{\sf{{\leadsto Volume \: of \: cube \: = \: (side)^{3}}}} \\  \\ {\sf{{\leadsto Diagonal \: of \: cube \: = \: \sqrt(l^{2} + b^{2} + h^{2})}}} \\  \\ {\sf{{\leadsto Perimeter \: of \: cube \: = \: 4(l+b+h)}}} \\ \\ {\sf{{\leadsto CSA \: of \: sphere \: = \: 2 \pi r^{2}}}} \\  \\ {\sf{{\leadsto SA \: of \: sphere \: = \: 4 \pi r^{2}}}} \\  \\{\sf{{\leadsto TSA \: of \: sphere \: = \: 3 \pi r^{2}}}} \\  \\ {\sf{{\leadsto Diameter \: of \: circle \: = \: 2r}}} \\  \\ {\sf{{\leadsto Radius \: of \: circle \: = \: \dfrac{d}{2}}}} \\  \\ {\sf{{\leadsto Volume \: of \: sphere \: = \: \dfrac{4}{3} \pi r^{3}}}} \\  \\ {\sf{{\leadsto Area \: of \: rectangle \: = \: Length \times Breadth}}} \\  \\ {\sf{{\leadsto Perimeter \: of \: rectangle \: = \:2(length+breadth)}}} \\  \\{\sf{{\leadsto Perimeter \: of \: square \: = \: 4 \times sides}}}\end{array}}}\end{gathered}\end{gathered}\end{gathered}$