Question

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

Answer 1

Volume-

`\tt\boxed{\tt \: 729 { \: centimetre}^(3) }`

TSA-

`\boxed{ \tt \: 486 \: centimetre {}^(2) }`

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:

`\tt \longmapsto \: 4a {}^(2) = 324 \: cm {}^(2)`

`\tt \longmapsto \: a {}^(2) = 81`

`\tt \longmapsto \: a = \: 9 \: centimetre`

• Therefore,TSA–

`\tt \longmapsto6a {}^(2)`

`\tt \longmapsto \: 6a * {9}^(2)`

`\tt \longmapsto \: 6 * 81`

`\tt \longmapsto \: 486 \: centimetre {}^(2)`

And, Volume–

`\tt \longmapsto{a {}^(2) }`

`\tt \longmapsto9³`

`\tt \longmapsto \: 729 { \: centimetre}^(3)`

Answer 2

Explanation:

Given :

• Lateral Surface Area of Cube = 324 cm²

`\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}}\end{gathered}`

To Find :

• Volume of the Cube = ?

• Total Surface Area of the Cube = ?

`\begin{gathered} \\ {\underline{\rule{200pt}{3pt}}}\end{gathered}</p><p>`

Solution :

~ Formula Used :

• Lateral Surface Area :

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

• Volume :

`\large{\red{\dashrightarrow}} \: \: {\underline{\boxed{\purple{\sf{ Volume{\small_((Cube))} = a³ }}}}}`

• Total Surface Area :

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

`\begin{gathered} \\ {\qquad{\rule{150pt}{1pt}}}\end{gathered}`

~ Calculating the Side :

`\\{\longmapsto{\qquad{\sf{ \cancel(324)/(4) = a² }}}}`

`{\longmapsto{\qquad{\sf{ LSA = 4a² }}}} \\ \\`

`{\longmapsto{\qquad{\sf{ 324 }}}}`

`\longmapsto{\qquad{\sf{ 81 = a²}}}`

`{\longmapsto{\qquad{\sf{ √(81) = a }}}} \\ \\`

`{\qquad{\textsf{ Side of the Cube = {\pink{\sf{ 9 \: cm}}}}}}`

`\begin{gathered} \\ {\qquad{\rule{150pt}{1pt}}}\end{gathered}`

~ Calculating the Volume :

`\begin{gathered}{ \red{\longmapsto{\qquad{\sf{ Volume = a³ }}}}} \\ \\ \ { \pink{\longmapsto{\qquad{\sf{ Volume = 9³ }}}} }\\ \\ \ { \green{\longmapsto{\qquad{\sf{ Volume = 9 * 9 * 9 }}}}} \\ \\ \ { \purple{\qquad{\textsf{ Volume of the Cube = {\green{\sf{ \boxed{\longmapsto \sf729 \: cm³ }}}}}}}}\end{gathered}`

~ Calculating the Total Surface Area :

`{\longmapsto{\qquad{\sf{ TSA = 6a² }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ TSA = 6 * 9² }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ TSA = 6 * 9 * 9 }}}}`

`{\longmapsto{\qquad{\sf{ TSA = 6 * 81 }}}} \\ \\ \ {\qquad{\textsf{ Total Surface Area of the Cube = {\red{\sf{ 486 \: cm² }}}}}}`

Therefore :

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

`\begin{gathered} \\ {\pink{\underline{\rule{75pt}{9pt}}}}{\blue{\underline{\rule{75pt}{9pt}}}}{\color{cyan}{\underline{\rule{75pt}{9pt}}}}\end{gathered}`