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Q.13.If the length,breadth and height of a cuboid are in the ratio5:3:2and its totalsurface area is1550sq.m. Find:(i)the dimensions of the cuboid (ii)volume of the cuboid.​

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Question:-

If the length,breadth and height of a CUBOID are in the ratio5:3:2and its total surface area is1550sq.m. Find:(i)the dimensions of the cuboid (ii)VOLUME of the cuboid.

Answer:-

  • The length, Breadth and height of cuboid is 25 m,15 m and 10 m.
  • The volume of cuboid is 3750 m³.

To find:-

  • the dimensions of the cuboid
  • volume of the cuboid.

Solution:-

  • Ratio = 5:3:2

Put x in the ratio,

  • Length = 5x
  • Breadth = 3x
  • Height = 2x
  • Total surface area = 1550 m²

(i)

\large { \mathfrak{ \green{ \underline{ \purple{ sa = 2(lb + bh + lh)}}}}}

where,

  • L = length
  • b = breadth
  • h = height

According to question,

\large{ \tt: \implies \: \: \: \: \: \: \: 2(lb + bh + lh) = 1550}

\large{ \tt : \implies \: \: \: \: \: 2(5x \times 3x + 3x \times 2x + 5x \times 2x) = 1550}

\large{ \tt : \implies \: \: \: \: \: 2(31 {x}^{2} ) = 1550}

\large{ \tt : \implies \: \: \: \: \: 31 {x}^{2} = \frac{1550}{2} } \\

\large{ \tt : \implies \: \: \: \: \: {x}^{2} = \frac{775}{31} } \\

\large{ \tt : \implies \: \: \: \: \: x = \sqrt{25} }

\large{ \tt : \implies \: \: \: \: \: x = 5 \: m}

  • The VALUE of x is 5 m
  • Length = 5x = 5×5 = 25 m
  • Breadth = 3x = 3×5 = 15 m
  • Height = 2x = 2×5 = 10 m

The length, Breadth and height of cuboid is 25 m,15 m and 10 m.

(ii)

\large { \mathfrak{ \green{ \underline{ \purple{ volume = l \times b \times h}}}}}

According to question,

\large{ \tt : \implies \: \: \: \: volume = 25 \times 15 \times 10}

\large{ \tt : \implies \: \: \: \: volume = 3750 \: {m}^{3} }

  • The volume of cuboid is 3750 m³.


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