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Qwerty90 Group Title

A triangular prism has a volume of 5 m3. If each dimension of the prism is tripled, what is the new volume of the prism?

  • 2 years ago
  • 2 years ago

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  1. Qwerty90 Group Title
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    Like would I need more values than this? I am trying to think of the formula for this

    • 2 years ago
  2. Directrix Group Title
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    135 cubic meters

    • 2 years ago
  3. Directrix Group Title
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    Cube the scale factor. (1/3)^3 = 1/27 ratio of original volume to volume of enlarged prism. 27*5 = 135

    • 2 years ago
  4. ash2326 Group Title
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    @Qwerty90 I'd showed you yesterday also. Volume= Area of base * height Area of base= \(\frac{\sqrt 3 a^2}{2}\) Height= h Volume= \[\frac{\sqrt 3 a^2}{2}\times h\] We are given volume as 5 m^3, so \[5=\frac{\sqrt 3 a^2}{2}\times h\] Now each of the dimensions are tripled so new side of equilateral triangle = 3a New height=3h Now Volume=\[\frac{\sqrt 3 (3a)^2}{2}\times 3h\] we get \[New Volume=9\times 3\frac{\sqrt 3 (a)^2}{2}\times h\] or \[New Volume=27 \times\frac{\sqrt 3 (a)^2}{2}\times h\] We know that \[5=\frac{\sqrt 3 a^2}{2}\times h\] so \[New Volume=27 \times5=135 m^3 \]

    • 2 years ago
  5. Qwerty90 Group Title
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    Thanks! and yes I did think about it and got my answer even before you got it so we were like mixing brains

    • 2 years ago
  6. Directrix Group Title
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    Scale Factor The ratio of any two corresponding lengths in two similar geometric figures. Note: The ratio of areas of two similar figures is the square of the scale factor. The ratio of volumes of two similar figures is the cube of the scale factor.

    • 2 years ago
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