Math, asked by samsung3322, 5 days ago

Find the surface area of a cube whose volume is 3375 cm³. Also find its diagonals.

Answers

Answered by tennetiraj86
15

Given :-

The volume of a cube is 3375 cm³

To find :-

i) The surface area of the cube .

ii) The length of the cube.

Solution :-

Given that

The volume of a cube = 3375 cm³

We know that

Volume of a cube whose length of its edge is a units is cubic units

Therefore, = 3375

=> a³ = 15³

=> a = 15

The length of the edge of the cube = 15 cm

We know that

Total Surface Area of a cube is 6a² sq.units

Total Surface Area of the cube = 6×15² cm²

=> TSA = 6×225 cm²

=> TSA = 1350 cm²

We know that

The length of the diagonal of a cube is 3 a units

The length of the diagonal of the given cube

= √3 × 15 cm

= 15√3 cm or

= 15×1.732 cm

= 25.98 cm

Answer :-

Total Surface Area of the cube

= 1350 cm²

The length of the diagonal of the cube

= 153 cm or 25.98 cm

Used formulae:-

Total Surface Area of a cube is 6a² sq.units

Volume of a cube whose length of its edge is a units is a³ cubic units

The length of the diagonal of a cube is √3 a units

Answered by saichavan
35

Given :

Volume of cube = 3375cm³

Volume of a cube whose length of its edge a is a³ cubic units.

 \sf \:  {a}^{3}  = 3375

 \sf \therefore \:  a = 15

\sf The \: length \: of \:edge \:of \:  cube \: is \:  \green{15cm}

 \sf \: Total \: surface \: area \: of \: cube \:  = 6 {a}^{2}

 \sf \therefore \: TSA \: of \: cube = 6 \times  {15}^{2}cm {}^{2} \\  \sf \:   \therefore \: TSA  \: of \: cube = 6  \times 225c{m}^{2}  \\  \sf \: TSA \: of \: cube = 1350cm {}^{2}

Length of diagonal of a cube is √2 a units.

 \sf \: Length \: of \: diagonal =  \sqrt{2}  \times 15

 \green{ \small \sf\implies Length \: of \: diagonal=15 \sqrt{2} cm}

Approximate value:

  \green{\sf \: Length \: of \: diagonal = 21.21cm}

_____________________________________

Additional information -

 \sf \: TSA \: of \: cube \:  = 6a {}^{2}

 \sf \: LSA \: of \: cube \:  = 4 \times side

 \footnotesize\sf \: Length \: of \: diagonal \: of \: cube \:  =  \sqrt{2} a \: units

 \sf Volume \: of \: cube \:  =  {a}^{3}

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