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Qwerty90
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?
Like would I need more values than this? I am trying to think of the formula for this
Cube the scale factor. (1/3)^3 = 1/27 ratio of original volume to volume of enlarged prism. 27*5 = 135
@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 \[New Volume=27 \times5=135 m^3 \]
Thanks! and yes I did think about it and got my answer even before you got it so we were like mixing brains
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.