Question

find the TSA LSA and Volume of cube whose sides are 3cm

full step by step explanation needed



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Answer 1

Answer:

The Total surface area (TSA) of cube is 54cm².

The Lateral surface area (LSA) of cube is 36cm².

The Volume of cube is 27cm³.

Step-by-step explanation:

Consider the provide information.

As per the provided information in the given question, we've been given that the side or edge of the cube is 3cm. With this information, we've been asked to find out the TSA, LSA and volume of the cube.

(i) The Total surface area (TSA) of cube:

Let a be the side or edge of the cube, then the Total surface area (TSA) of cube is given by,

→ TSA = 6a²

where, a is the side or edge of the cube.

By substituting the given value in the formula, we get:

→ TSA = 6(3)²

→ TSA = 6(9)

→ TSA = 54

Hence, the total surface area of cube is 54cm².

(ii) The Lateral surface area (LSA) of cube:

Let a be the side or edge of the cube, then the Lateral surface area (TSA) of cube is given by,

→ LSA = 4a²

where, a is the side or edge of the cube.

By substituting the given value in the formula, we get:

→ LSA = 4(3)²

→ LSA = 4(9)

→ LSA = 36

Hence, the lateral surface are of cube is 36cm².

(iii) The volume of cube:

Let a be the side or edge of the cube, then the Volume of cube is given by,

→ Volume = a³

where, a is the side or edge of the cube.

By substituting the given value in the formula, we get:

→ Volume = (3)³

→ Volume = 27

Hence, the volume of cube is 27cm³.

Answer 2

Answer:

Diagram :

$\setlength{\unitlength}{4mm}\begin{picture}(10,6)\thicklines\put(0,1){\line(0,1){10}}\put(0,1){\line(1,0){10}}\put(10,1){\line(0,1){10}}\put(0,11){\line(1,0){10}}\put(0,11){\line(1,1){5}}\put(10,11){\line(1,1){5}}\put(10,1){\line(1,1){5}}\put(0,1){\line(1,1){5}}\put(5,6){\line(1,0){10}}\put(5,6){\line(0,1){10}}\put(5,16){\line(1,0){10}}\put(15,6){\line(0,1){10}}\put(4.6,-0.5){\bf\large{3\ cm}}\put(13.5,3){\bf\large{3\ cm}}\put(-4,5.8){\bf\large{3\ cm}}\end{picture}$

The diagram of cylinder is given above. See this latex diagram on website Brainly.in.

$\begin{gathered}\end{gathered}$

Given :

• ➞ Side of cube = 3 cm

$\begin{gathered}\end{gathered}$

To Find :

• ➞ TSA of cube
• ➞ LSA of cube
• ➞ Volume of cube

$\begin{gathered}\end{gathered}$

Using Formulas :

$\longrightarrow\small{\underline{\boxed{\sf{TSA \: of \: cube = 6(a)^{2} }}}}$

$\longrightarrow\small{\underline{\boxed{\sf{LSA \: of \: cube = 4(a)^{2} }}}}$

$\longrightarrow\small{\underline{\boxed{\sf{Volume \: of \: cube = {(a)}^{3}}}}}$

Where :

• ➟ a = side
• ➟ TSA = Total surface area
• ➟ LSA = Lateral surface area

$\begin{gathered}\end{gathered}$

Solution :

Finding the TSA of cube by substituting the values in the formula :

$\longrightarrow \: \: {\sf{TSA \: of \: cube = 6(a)^{2}}}$

$\longrightarrow \: \: {\sf{TSA \: of \: cube = 6(3)^{2}}}$

$\longrightarrow \: \: {\sf{TSA \: of \: cube = 6(3 \times 3)}}$

$\longrightarrow \: \: {\sf{TSA \: of \: cube = 6(9)}}$

$\longrightarrow \: \: {\sf{TSA \: of \: cube = 6 \times 9}}$

$\longrightarrow \: \: {\sf{TSA \: of \: cube = 54 \: {cm}^{2}}}$

$\bigstar \: {\purple{\underline{\boxed{\sf{TSA \: of \: cube = 54 \: {cm}^{2}}}}}}$

∴ The TSA of cube is 54 cm².

$\rule{300}{1.5}$

Finding LSA of cube by substituting the values in the formula :

$\longrightarrow \: \:{\sf{LSA \: of \: cube = 4(a)^{2}}}$

$\longrightarrow \: \:{\sf{LSA \: of \: cube = 4(3)^{2}}}$

$\longrightarrow \: \:{\sf{LSA \: of \: cube = 4(3 \times 3)}}$

$\longrightarrow \: \:{\sf{LSA \: of \: cube = 4(9)}}$

$\longrightarrow \: \:{\sf{LSA \: of \: cube = 4 \times 9}}$

$\longrightarrow \: \:{\sf{LSA \: of \: cube = 36 \: {cm}^{2}}}$

$\bigstar \:{\purple{\underline{\boxed{\sf{LSA \: of \: cube = 36 \: {cm}^{2}}}}}}$

∴ The LSA of cube is 36 cm².

$\rule{300}{1.5}$

Finding volume of cube by substituting the values in the formula :

$\longrightarrow \: \: {\sf{Volume \: of \: cube = {(a)}^{3}}}$

$\longrightarrow \: \: {\sf{Volume \: of \: cube = {(3)}^{3}}}$

$\longrightarrow \: \: {\sf{Volume \: of \: cube = {(3 \times 3 \times 3)}}}$

$\longrightarrow \: \: {\sf{Volume \: of \: cube = {(27)}}}$

$\longrightarrow \: \: {\sf{Volume \: of \: cube = 27 \: {cm}^{3}}}$

$\bigstar \: {\purple{\underline{\boxed{\sf{Volume \: of \: cube = 27 \: {cm}^{3}}}}}}$

∴ The volume of cube is 27 cm³.

$\begin{gathered}\end{gathered}$

Learn More :

$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area formula\\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt 1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}$

$\rule{220pt}{3pt}$