Question

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

Answer 1

Step-by-step 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 = ?

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

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 :

$\\{\longmapsto{\qquad{\sf{ \cancel\dfrac{324}{4} = a² }}}}$

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

${\longmapsto{\qquad{\sf{ 324 }}}}$

$\longmapsto{\qquad{\sf{ 81 = a²}}}$

${\longmapsto{\qquad{\sf{ \sqrt{81} = a }}}}$

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

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

~ Calculating the  Volume :

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

~ Calculating the Total Surface Area :

${\longmapsto{\qquad{\sf{ TSA = 6a² }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ TSA = 6 \times 9² }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ TSA = 6 \times 9 \times 9 }}}}$

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

Therefore :

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

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

Answer 2

Answer:

Volume-

$\tt\boxed{\tt \: 729 { \: centimetre}^{3} }$

TSA-

$\boxed{ \tt \: 486 \: centimetre {}^{2} }$

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:

$\tt \longmapsto \: 4a {}^{2} = 324 \: cm {}^{2}$

$\tt \longmapsto \: a {}^{2} = 81$

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

• Therefore,TSA–

$\tt \longmapsto6a {}^{2}$

$\tt \longmapsto \: 6a \times {9}^{2}$

$\tt \longmapsto \: 6 \times 81$

$\tt \longmapsto \: 486 \: centimetre {}^{2}$

And, Volume–

$\tt \longmapsto{a {}^{2} }$

$\tt \longmapsto9³$

$\tt \longmapsto \: 729 { \: centimetre}^{3}$