Question

if the volume of cube is 1331cm^3find side of cube and length of diagonal​

Answer 1

Given:

• Volume = 1331 cm³

To find:

➤ Side of cube = ?

➤ Length of diagonal = ?

Method:

First let's understand the formulas;

➩ Volume = (Side)³

➩ Length of diagonal = √3 × Side

Solution:

Volume = (Side)³

➝ 1331 = (Side)³

➝ Side = ∛1331

➝ Side of cube = 11 cm

Length of diagonal = √3 × Side

➞ Length of diagonal = √3 × 11

➞ Length of diagonal = 11 √3 cm

Know more:

$\begin{array}{|c|c|c|}\cline{1-3}\bf Shape&\bf Volume\ formula&\bf Surface\ area \\\cline{1-3}\sf Cube&\tt l^3}&\tt 6l^2\\\cline{1-3}\sf Cuboid&\tt lbh&\tt 2(lb+bh+lh)\\\cline{1-3}\sf Cylinder&\tt {\pi}r^2h&\tt 2\pi{r}(r+h)\\\cline{1-3}\sf Hollow\ cylinder&\tt \pi{h}(R^2-r^2)&\tt 2\pi{rh}+2\pi{Rh}+2\pi(R^2-r^2)\\\cline{1-3}\sf Cone&\tt1/3\ \pi{r^2}h&\tt \pi{r}(r+s)\\\cline{1-3}\sf Sphere&\tt 4/3\ \pi{r}^3&\tt 4\pi{r}^2\\\cline{1-3}\sf Hemisphere&\tt 2/3\ \pi{r^3}&\tt 3\pi{r}^2\\\cline{1-3}\end{array}$

Answer 2

${\bold{\sf{\underline{Understanding \: the \: question}}}}$

✠ This question says that there is a cube given and it's volume is 1331 cm² And now this question ask us to find the side of cube and the length of diagonal. It's diagram is given below :

${\bold{\pink{\sf{Diagram \: of \: cube \: showing \: measures}}}}$

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

${\bold{\pink{\sf{Diagram \: of \: cube \: showing \: measures}}}}$

Please see attachment to know where is diagnol length. As u see in diagram that a line cut the cube it's diagonal length

${\bold{\sf{\underline{Given \: that}}}}$

✠ Volume of cube = 1331 cm³

${\bold{\sf{\underline{To \: find}}}}$

✠ Side of cube

✠ Length of diagonal

${\bold{\sf{\underline{Solution}}}}$

✠ Side of cube = 11 cm

✠ Length of diagonal = 11 √3 cm.

${\bold{\sf{\underline{Using \: concepts}}}}$

✠ Volume of cube formula

✠ Length of diagonal formula

${\bold{\sf{\underline{Using \: formulas}}}}$

✠ Volume of cube formula = a³

Note : a denotes Sides !

✠ Length of diagonal formula = √3 × Side

${\bold{\sf{\underline{Procedure \: of \: the \: question}}}}$

✠ To solve this problem firstly we have to use the formula to find volume of cube. Now we have to put the values and we get the side of given cube. Afterthat we have to use the formula to find the length of diagonal .Now we have to put the values and we get length of diagonal.

${\bold{\sf{\underline{Solution}}}}$

☞ Finding side of cube :

↦ Volume = a³

↦ 1331 = a³

↦ ∛1331 = a

↦ a = ∛1331

↦ a = 11

• Therefore, the side of given cube is 11

☞ Finding length of diagonal :

↦ Length of diagonal = √3 × Side

↦ Length of diagonal = √3 × 11

↦ Length of diagonal = 11 √3 cm

• Therefore, length of diagonal is 11 √3 cm.

${\bold{\sf{\underline{Knowledge \: booster}}}}$

${\bold{\pink{\sf{Diagram \: of \: cube}}}}$

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

${\bold{\pink{\sf{Formulas \: related \: to \: volume \: and \: surface \: areas}}}}$

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

${\bold{\pink{\sf{Formula \: related \: to \: cube}}}}$ -

$\boxed{\begin{minipage}{6.2 cm}\bigstar \:\underline{\textbf{Formulae Related to Cube :}}\\\\\sf {\textcircled{\footnotesize\textsf{1}}} \:\: Lateral \: Surface \: Area =4(side)^{2}\\\\\sf{\textcircled{\footnotesize\textsf{2}}} \:\:Total \: Surface \: Area = 6(side)^{2}\\ \\{\textcircled{\footnotesize\textsf{3}}} \: \:Volume= \: a^{3}\end{minipage}}$

Request - Please see this answer from web browser or chrome because there are some diagrams or formulas given here by me and these are not shown here clearly that's why I request that please see it from web. Thank you.