Question

Find The curved surface Area Total surface Area vertical surface Area and volume of a cube with side 6 cm​

Answer 1

Correct question :

Find the curved surface area,total surface area and volume of cube whose side is 6cm.

Given :

• Side of cube = 6cm

To find :

• Curved surface area of cube
• T.S.A of cube
• Volume of cube

Formulae to remember :

• C.S.A of cube = 4 × (side)²
• T.S.A of cube = 6 × (side)²
• Volume of cube = (side)³

Solution :

• ✦ Curved surface area of cube = 4(side)²

➯ 4 × (6)²

➯ 4 × 36

➯ 144 cm²

• ✦ T.S.A of cube = 6(side)²

➯ 6 (6)²

➯ 6 (36)

➯ 216 cm²

• ✦ Volume of cube = side³

➯ (6)³

➯ 216 cm³

Answer 2

Given: Side of the cube is 6cm.

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$\dag \: \frak{ Need \: to \: find} \begin{cases} \frak{ Total \: surface \: area} \\ \\ \frak {Lateral \: Surface \: area} \\ \\ \frak{ Volume}\end {cases}$

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$\star$ As we know that,

• Total surface area = $\sf 6 {s}^{2}$

• Lateral surface area = $\sf 4 {s}^{2}$

• Volume = $\sf {s}^{3}$

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$\begin{gathered}\bigstar\:{\underline{\sf{\pmb{According\:to\:the\:Question\::}}}}\\\\\end{gathered}$

Now, We can calculate TSA , LSA & volume by using the formula's given above,

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$\begin{gathered}\bigstar\:{\underline{\sf{\pmb{Total\:surface\:area\::}}}}\\\\\end{gathered}$

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$: \implies \sf{6 \times {6}^{2} } \\ \\ \\ : \implies \sf{6 \times 36} \\ \\ \\ \begin{gathered} :\implies{\boxed{\underline{ \frak{ \purple{ 216 \: {cm}^{2}}}}}}\:\bigstar \\ \\\end{gathered}$

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$\begin{gathered}\bigstar\:{\underline{\sf{\pmb{Lateral\:surface\:area\::}}}}\\\\\end{gathered}$

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$: \implies \sf{4 \times {6}^{2} } \\ \\ \\ : \implies \sf{4 \times 36} \\ \\ \\ \begin{gathered} :\implies{\boxed{\underline{ \frak{ \purple{ 144 \: {cm}^{2}}}}}}\:\bigstar \\ \\\end{gathered}$

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$\begin{gathered}\bigstar\:{\underline{\sf{\pmb{Volume\::}}}}\\\\\end{gathered}$

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$\begin{gathered} : \implies \sf{{6}^{3}} \\ \\ \\ :\implies{\boxed{\underline{ \frak{ \purple{ 216 \: {cm}^{3}}}}}}\:\bigstar \\ \\\end{gathered}$

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${\therefore\:{\underline{\sf{Hence,\:TSA , LSA \: and \: Volume \: are\: {\pmb{\sf{216 \: {cm}^{2}}}}, \pmb{144 \: {cm}^{2}} {\sf{and \: }} \pmb{216 \: {cm}^{3}}}}}}$

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$\begin{gathered}\qquad\qquad\boxed{\underline{\underline{\pink{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}} \\\end{gathered}$

• Curved surface area of cube = 4a²

• Total surface area of cube = 6a²

• Volume of cube = a³

• Curved surface area of cuboid = 2(l + b)h

• Total surface area cuboid = 2(lb + bh + hl)

• Volume of cuboid = l × b × h