Question

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?

Answer 1

Like would I need more values than this? I am trying to think of the formula for this

Answer 2

135 cubic meters

Answer 3

Cube the scale factor. (1/3)^3 = 1/27 ratio of original volume to volume of enlarged prism. 27*5 = 135

Answer 4

@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
\[New Volume=27 \times5=135 m^3 \]

Answer 5

Thanks! and yes I did think about it and got my answer even before you got it so we were like mixing brains

Answer 6

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.