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The lateral surface area of a cube is 324 cm ² . Find its volume and total surface area​​

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YourHelperAdiidn

Step-by-step explanation:

Given :

  • Lateral Surface Area of Cube = 324 cm²

[tex]\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}}\end{gathered}[/tex]

To Find :

  • Volume of the Cube = ?

  • Total Surface Area of the Cube = ?

[tex]\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}}\end{gathered}

[/tex]

Solution :

~ Formula Used :

  • Lateral Surface Area :

[tex]{\red{\dashrightarrow}} \: \: {\underline{\boxed{\purple{\sf{ Lateral \: Surface \: Area {\small_{(Cube)}} = 4 a² }}}}}[/tex]

  • Volume :

[tex]\large{\red{\dashrightarrow}} \: \: {\underline{\boxed{\purple{\sf{ Volume{\small_{(Cube)}} = a³ }}}}}[/tex]

  • Total Surface Area :

[tex]\large{\red{\dashrightarrow}} \: \: {\underline{\boxed{ \red{\sf{ Total \: Surface \: Area {\small_{(Cube)}} = 6a² }}}}}[/tex]

[tex]\begin{gathered} \\ {\qquad{\rule{150pt}{1pt}}}\end{gathered}[/tex]

~ Calculating the Side :

[tex]\\{\longmapsto{\qquad{\sf{ \cancel\dfrac{324}{4} = a² }}}}[/tex]

[tex]{\longmapsto{\qquad{\sf{ LSA = 4a² }}}} \\ \\ [/tex]

[tex] {\longmapsto{\qquad{\sf{ 324 }}}}[/tex]

[tex]\longmapsto{\qquad{\sf{ 81 = a²}}}[/tex]

[tex]{\longmapsto{\qquad{\sf{ \sqrt{81} = a }}}} \\ \\ [/tex]

[tex]{\qquad{\textsf{ Side of the Cube = {\pink{\sf{ 9 \: cm}}}}}}[/tex]

[tex]\begin{gathered} \\ {\qquad{\rule{150pt}{1pt}}}\end{gathered}[/tex]

~ Calculating the  Volume :

[tex]\begin{gathered}{ \red{\longmapsto{\qquad{\sf{ Volume = a³ }}}}} \\ \\ \ { \pink{\longmapsto{\qquad{\sf{ Volume = 9³ }}}} }\\ \\ \ { \green{\longmapsto{\qquad{\sf{ Volume = 9 \times 9 \times 9 }}}}} \\ \\ \ { \purple{\qquad{\textsf{ Volume of the Cube = {\green{\sf{ \boxed{\longmapsto \sf729 \: cm³ }}}}}}}}\end{gathered}[/tex]

~ Calculating the Total Surface Area :

[tex]{\longmapsto{\qquad{\sf{ TSA = 6a² }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ TSA = 6 \times 9² }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ TSA = 6 \times 9 \times 9 }}}} [/tex]

[tex]{\longmapsto{\qquad{\sf{ TSA = 6 \times 81 }}}} \\ \\ \ {\qquad{\textsf{ Total Surface Area of the Cube = {\red{\sf{ 486 \: cm² }}}}}}[/tex]

Therefore :

  • ❝ Volume of the Cube is 729 cm³ and it's Total Surface Area is 486 cm² .❞

[tex]\begin{gathered} \\ {\pink{\underline{\rule{75pt}{9pt}}}}{\blue{\underline{\rule{75pt}{9pt}}}}{\color{cyan}{\underline{\rule{75pt}{9pt}}}}\end{gathered}[/tex]

Sᴘᴀᴄᴇ7idn

Answer:

Volume-

[tex]\tt\boxed{\tt \: 729 { \: centimetre}^{3} }[/tex]

TSA-

[tex]\boxed{ \tt \: 486 \: centimetre {}^{2} }[/tex]

Step-by-step explanation:

Let the length of each edge of a cube be a centimetre(cm)

Given,

LSA of the cube is 324cm^2

Answer with explanation:

[tex] \tt \longmapsto \: 4a {}^{2} = 324 \: cm {}^{2} [/tex]

[tex] \tt \longmapsto \: a {}^{2} = 81[/tex]

[tex] \tt \longmapsto \: a = \: 9 \: centimetre[/tex]

  • Therefore,TSA–

[tex] \tt \longmapsto6a {}^{2} [/tex]

[tex]\tt \longmapsto \: 6a \times {9}^{2} [/tex]

[tex]\tt \longmapsto \: 6 \times 81[/tex]

[tex]\tt \longmapsto \: 486 \: centimetre {}^{2} [/tex]

And, Volume–

[tex]\tt \longmapsto{a {}^{2} }[/tex]

[tex]\tt \longmapsto9³ [/tex]

[tex]\tt \longmapsto \: 729 { \: centimetre}^{3} [/tex]

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