Question

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?

Answer 1

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:

$H=6 cm\\b=4 cm\\h=8cm$

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:

$A_t_r_i_a_n_g_l_e=\frac{b*h}{2}$

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

$V=A_t_r_i_a_n_g_l_e*H=\frac{b*h}{2}*H\\ V=\frac{6cm*4cm}{2}*8cm= 96cm^3$

If all dimensions are tripled, the new volume is:

$V=\frac{3*b*3*h}{2}*3*H\\ V=\frac{3*6cm*3*4cm}{2}*3*8cm=2592 cm^3$

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

$\frac{2592}{96}= 27$

It means that the original volume increased 27 times.

Answer 2

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