Question

if the volume of cube is 1331cm^3find side of cube an
d length o

f diagonal​

Answer 1

Answer:

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

Answer 2

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$\star \: \bf\underbrace{Correct\:Question} \: \star$

• If the volume of cube is 1331cm³ find side of cube and length of diagonal_?

Diagram of cube showing measures:-

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

$\text{\large\underline{\red{Given:-}}}$

• Volume = 1331 cm³

$\text{\large\underline{\orange{To Find:-}}}$

• Side of cube = ?
• Length of diagonal = ?

$\text{\large\underline{\purple{Solution:-}}}$

• Side of cube = 11 cm
• Length of diagonal = 11 √3 cm.

Using Consepts

• Volume of cube formula
• Length of diagonal formula

Using Formula:-

• Volume of cube formula = a³
• Length of diagonal formula = √3 × Side

$\text{\large\underline{\pink{Procedure of the question-}}}$

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.

Explaination :-

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.

$\star \: \bf\underbrace{To\: Know\: More:-} \: \star$

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

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