Math, asked by psaulakh, 4 months ago

find the edge of a cube whose lateral surface area is 1156 cm2.​

Answers

Answered by Sen0rita
41

Given : Lateral surface area of a cube is 1156cm².

To Find : Edge of the cube.

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Here

 \:  \:

  • Lateral surface area of the cube = 1156 cm²

 \:  \:

We've to find the edge of the cube.

 \:  \:

❍ To find the edge of the cube, we've to put the lateral surface area in the formula.

 \:

As we know that -

 \:  \:

\star \:  \: \underline{\boxed{\sf\pink{L.S.A \: of \: a \: cube \:  = 4 {a}^{2} }}} \:

 \:  \:

❍ Where, a denotes edge of the cube.

 \:

Now,

 \:  \:

\sf:\implies \: L.S.A \: of \: the \: cube \:  = 4 {a}^{2}  \\  \\  \\ \sf:\implies \: 1156 = 4 {a}^{2}  \\  \\  \\ \sf:\implies \:  {a}^{2}  =  \cancel\frac{1156}{4}  \\  \\  \\ \sf:\implies \:  {a}^{2}  = 289 \\  \\  \\ \sf:\implies \:  a =  \sqrt{289}  \\  \\  \\ \sf:\implies \: \underline{\boxed{\mathfrak\purple{a = 17cm}}} \: \bigstar \\  \\  \\  \\ \sf\therefore{\underline{Hence, \: the \: edge \: of \: the \: cube \: is \: \bold{17 \: cm}.}}

Answered by Anonymous
40

Given:

  • The lateral surface area of a cube = 1156cm²

 \\

To Find:

  • the edge of the following cube

 \\

Solution:

~here, We have been provided with the lateral surface area of a cube and it is said to find its edge.

so, what do we do now?

Now, We are gonna apply suitable formulae with the given clues and such that we will find its edge

The Formula to find the lateral surface area:

\tt \longrightarrow l.s.a \: of \: a \: cube \:  = 4(edge^{2} )

Now, let's substitute the value of the lateral surface area and find its edge :

\tt \longrightarrow l.s .a = 4() ^{2}  \\  \\  \\\tt \longrightarrow  1156  = 4( {l}^{2} ) \:  \:  \\  \\  \\ \tt \longrightarrow  {l}^{2}  = \cancel  \frac{1156}{4}  \:  \:  \:  \:  \:  \\  \\  \\ \tt \longrightarrow  {l}^{2}  = 289 \:  \:  \:  \:  \:  \:  \:  \:  \\  \\  \\ \tt \longrightarrow  \: l =  \sqrt{289}  \:  \:  \:  \:  \:  \\  \\  \\ \longrightarrow { \underline{ \boxed{ \frak{  \pink{l = 17cm}}}} \bigstar} \:  \:

 \\

Hence:

  • the lateral surface area of the cube = 17cm

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