Math, asked by phdeathmark, 6 hours ago

A rectangular metal box has dimensions of 3 cm. 5 cm, and 8 cm. The
new volume is 72 cm³ larger than the old volume if the first two dimensions are
increased by the same number of centimeters and the third dimension
remains unchanged. What is the new dimension of the rectangular metal box
that has been enlarged?​

Answers

Answered by madhuse38
13

Answer:

Premieter of rectangular = 3cm ×(L+b)

= 3cm×5cm+8cm

= 3cm×13

= 39cm

The volume =72cm³×39cm

= 2808cm⁴

Hence,

The answer is 2808 .

Answered by PoojaBurra
3

Given: A rectangular metal box has dimensions of 3 cm. 5 cm, and 8 cm. The  new volume is 72 cm³ larger than the old volume.

To find: The new dimension of the rectangular metal box that has been enlarged.

Solution:

  • Let the number of centimetres by which each of the first two dimensions are increased be equal to x.
  • According to the question,

        V_{new} = 72cm^{3} + V_{old}

  • Here, V_{new} is the new volume and V_{old} is the old volume.
  • So, the old volume is calculated as follows,

        V_{old} = 3cm * 5cm * 8cm

               = 120cm^{3}

  • And, the new volume is calculated as follows,

        V_{new} = (3+x) * (5+x) * 8

                = 8x^{2} + 64x + 120

  • When added these values to the equation formed,

         8x^{2} + 64x + 120 = 72cm^{3} + 120cm^{3}

  • On solving, the value of x is found to be,

         x = 1 or x = -9

  • The value 1 is considered since the negative value is cannot be considered.
  • The first two dimentions are,

        3 + x = 4cm

        5 + x = 6cm

Therefore, the new dimension of the rectangular metal box that has been enlarged is 4 cm, 6 cm and 8 cm.

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