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

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)`

Answer 2

The volume increased 27 times of its original value.

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=(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=(b*h)/(2)*H\\ V=(6cm*4cm)/(2)*8cm= 96cm^3`

If all dimensions are tripled, the new volume is:

`V=(3*b*3*h)/(2)*3*H\\ V=(3*6cm*3*4cm)/(2)*3*8cm=2592 cm^3`

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

`(2592)/(96)= 27`

It means that the original volume increased 27 times.