A triangular prism has a base that is 6 cm by 4 cm and a height of 8 cm. If all dimensions are tripled, what happens to the volume?

Im assuming the base of the triangle is 4cm. The volume is [tex]96cm^{3}[/tex].
If the dimensions are tripled, the base is 12, the height is 24, and the length is 18. The volume is [tex]2592cm^{3}[/tex], which is 27 times bigger.
If you are increasing each side by a factor of x, you are multiplying the original by [tex] x^{3} [/tex]

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rmanquelafquen rmanquelafquen · Answer 2 · 2019-08-17T23:28:37+02:00

Answer:

The volume increased 27 times of its original value.

Step-by-step explanation:

Firstly, i have attached an image that it represents the form of a triangular prism.

So, if we use the same variables from the image, the values of each one are:

[tex]H=6 cm\\b=4 cm\\h=8cm[/tex]

In order to determine the volume of a triangular prism, we need to determine the area of the triangular face of the triangular prism.

The area of the triangular face is:

[tex]A_t_r_i_a_n_g_l_e=\frac{b*h}{2}[/tex]

Then, the area of the triangular face is multiplying by the length of the triangular prism, H, to get its volume:

[tex]V=A_t_r_i_a_n_g_l_e*H=\frac{b*h}{2}*H\\ V=\frac{6cm*4cm}{2}*8cm= 96cm^3[/tex]

If all dimensions are tripled, the new volume is:

[tex]V=\frac{3*b*3*h}{2}*3*H\\ V=\frac{3*6cm*3*4cm}{2}*3*8cm=2592 cm^3[/tex]

Finally, if we divide the new volumen by the original volume, the value is:

[tex]\frac{2592}{96}= 27[/tex]

It means that the original volume increased 27 times.