Question

Find the volime, Total surface area and lateral surface area of a cube of edge 10cm​

Answer 1

Question :-

Find the volume, total surface area and lateral surface area of a cube of edge 10 cm.

$\large\underline{\sf{Solution-}}$

Given that,

Edge of the cube, x = 10 cm

We know that,

$\boxed{ \rm{ \:Volume_{(cube)} \: = \: {(edge)}^{3} \: }}$

So,

$\rm \: Volume_{(cube)} = {(10)}^{3}$

$\red{\rm\implies \:Volume_{(cube)} \: = \: 1000 \: {cm}^{3} \: \: }$

Now, we know that

Lateral surface area (LSA) of a cube is given by

$\boxed{ \rm{ \:LSA_{(cube)} \: = \: {4(edge)}^{2} \: }}$

So,

$\rm \: LSA_{(cube)} \: = \: 4 \times {(10)}^{2}$

$\rm \: LSA_{(cube)} \: = \: 4 \times 100$

$\red{\rm\implies \:LSA_{(cube)} \: = \: 400 \: {cm}^{2}}$

Now, we know

Total Surface Area (TSA) is given by

$\boxed{ \rm{ \:TSA_{(cube)} \: = \: 6 \times {(edge)}^{2} \: }}$

So,

$\rm \: TSA_{(cube)} \: = \: 6 \times {(10)}^{2}$

$\rm \: TSA_{(cube)} \: = \: 6 \times 100$

$\red{\rm\implies \:TSA_{(cube)} \: = \: 600 \: {cm}^{2} \: }$

Hence,

$\begin{gathered}\begin{gathered}\bf\: \begin{cases} &\sf{Volume_{(cube)} = 1000 \: {cm}^{3} } \\ \\ &\sf{LSA_{(cube)} = 400 \: {cm}^{2} }\\ \\ &\sf{TSA_{(cube)} = 600 \: {cm}^{2} } \end{cases}\end{gathered}\end{gathered}$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{CSA_{(cylinder)} = 2\pi \: rh}\\ \\ \bigstar \: \bf{Volume_{(cylinder)} = \pi {r}^{2} h}\\ \\ \bigstar \: \bf{TSA_{(cylinder)} = 2\pi \: r(r + h)}\\ \\ \bigstar \: \bf{CSA_{(cone)} = \pi \: r \: l}\\ \\ \bigstar \: \bf{TSA_{(cone)} = \pi \: r \: (l + r)}\\ \\ \bigstar \: \bf{Volume_{(sphere)} = \dfrac{4}{3}\pi {r}^{3} }\\ \\ \bigstar \: \bf{Volume_{(cube)} = {(side)}^{3} }\\ \\ \bigstar \: \bf{CSA_{(cube)} = 4 {(side)}^{2} }\\ \\ \bigstar \: \bf{TSA_{(cube)} = 6 {(side)}^{2} }\\ \\ \bigstar \: \bf{Volume_{(cuboid)} = lbh}\\ \\ \bigstar \: \bf{CSA_{(cuboid)} = 2(l + b)h}\\ \\ \bigstar \: \bf{TSA_{(cuboid)} = 2(lb +bh+hl )}\\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$

Answer 2

Question :-

• Find the Volume, Total Surface Area and Lateral Surface Area of a Cube of Edge 10 cm .

⠀⠀⠀⠀⠀⠀⠀

Answer :-

• Volume = 1000 cm³ .
• Total Surface Area = 600 cm² .
• Lateral Surface Area = 400 cm² .

⠀⠀⠀⠀⠀⠀⠀

Explanation :-

⠀⠀⠀⠀⠀⠀⠀

● First, we will find the Volume :-

$\Longrightarrow \: \sf{ Volume \: _{Cube} = ( \: edge \: ) {}^{3} }$

$\Longrightarrow \: \sf{Volume \: _{Cube} = ( \: 10 \: ) {}^{3} }$

$\Longrightarrow \: \sf{Volume \: _{Cube} = 1000 \: {cm}^{3} }$

⠀⠀⠀⠀⠀⠀⠀

● Now, we will find Total Surface Area :-

$\Longrightarrow \: \sf{ T.S.A \: _{Cube} = 6 \times ( \: edge \: ) {}^{2} }$

$\Longrightarrow \: \sf{T.S.A \: _{Cube} = 6 \times ( \: 10 \: ) {}^{2} }$

$\Longrightarrow \: \sf{T.S.A \: _{Cube} = 6 \times 100}$

$\Longrightarrow \: \sf{T.S.A \: _{Cube} = 400 \: cm {}^{2} }$

⠀⠀⠀⠀⠀⠀⠀

● Here, let's find Lateral Surface Area :-

$\Longrightarrow \: \sf{ L.S.A \: _{Cube} = 4 \times ( \: edge \: ) {}^{2} }$

$\Longrightarrow \: \sf{L.S.A \: _{Cube} = 4 \times ( \: 10 \: ) {}^{2} }$

$\Longrightarrow \: \sf{L.S.A \: _{Cube} = 4 \times 100}$

$\Longrightarrow \: \sf{L.S.A \: _{Cube} = 400 \: {cm}^{2} }$

⠀⠀⠀⠀⠀⠀⠀

Hence :-

• Volume is 1000 cm³ .
• Total Surface Area is 600 cm² .
• Lateral Surface Area is 400 cm² .

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃

$\begin{gathered}\begin{gathered}\boxed{\begin{array}{c} \\ \underline{ { \pmb {\sf \red{ \dag \: \: More \: Formulas \: \: \dag}}}} \\ \\ \\ \footnotesize \bigstar \: \sf{Volume = ( \: edge \: ) {}^{3} } \\ \\ \\ \footnotesize \bigstar \: \sf{Total \: Surface \: Area = 6 \times ( \: edge \: ) {}^{2} } \\ \\ \\ \footnotesize \bigstar \: \sf{Lateral \: Surface \: Area = 4 \times ( \: edge \: ) {}^{2} } \\ \\ \\ \footnotesize \bigstar \: \sf{Diagonal = ( \: edge \: \sqrt{3} \: )}\end{array}}\end{gathered}\end{gathered}$