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Mario has a rectangular prism completely filled with sand that has a base area of 85 cm² and a height of 15 cm. Mario pours all of its contents into a second rectangular prism that has a height of 25 cm. The sand completely fills the second rectangular prism. What is the base area of this second rectangular prism? Enter your answer in the box.

Respuesta :

The base area of the second rectangular prism is 51 cm²

The rectangular prism completely filled with sand has a base area of 85cm² and height of 15cm .

Volume of a rectangular prism

  • volume = Bh

where

B = base area

h = height

Since the first rectangular prism was completely filled with sand and it completely filled the second rectangular prism, it means they both have the same volume.

Therefore,

volume of the first rectangular prism = volume of the second rectangular prism.

  • volume  = Bh
  • volume = 85 × 15
  • volume = 1275 cm³

Therefore, the base area of the second rectangular prism can be calculated as follows:

volume = Bh

1275 = 25B

B = 1275 / 25

B = 51 cm²

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