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garri49 [273]
3 years ago
13

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 volu

me?

Mathematics
2 answers:
Naddik [55]3 years ago
6 0

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.

<u>The area of the triangular face</u> 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 <em>new volume</em> 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 <em>new volumen</em> by the <em>original volume</em>, the value is:

\frac{2592}{96}= 27

It means that the original volume increased 27 times.

lana [24]3 years ago
3 0
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}
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