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An architect is planning to make two triangular prisms out of iron. The architect will use ∆ABC for the bases of one prism and ∆DEF for the bases of the other prism.
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(a) What is the scale factor from ∆ABC to ∆DEF?

(b) Suppose the height of the prism made by ∆ABC is 15 centimeters. What is the volume of the prism made by ∆ABC? Remember to show your work.

(c) Suppose the volume of the prism made by ∆ABC is 4459 cm^3. What is the volume of the prism made by ∆DEF? Remember to show your work.

An architect is planning to make two triangular prisms out of iron The architect will use ABC for the bases of one prism and DEF for the bases of the other pris class=

Respuesta :

a) 5/7

b) 4459 cm cube

c) 2275 cm cube

Step-by-step explanation:

Step 1 :

a)

The Side AB (28 cm) has been scaled to side DE (20 cm)

Let x b the scale factor.

Then we have 28 *x = 20

=> x = 20/28 = 5/7

Hence the scale factor is 5/7

Step 2 :

b)

Given the height of the triangular prism is 15 cm

Volume = ( 1/2 ) * base* height of the triangle * height of the prism

= (1/2)* 21*28*15 = 4410 cm cube.

Step 3 :

c)

Given volume of the triangular prism with base ABC is 4459 cm cube

The scale factor is 5/7

Hence the volume of the prism with DEF as base is

4459 * (5/7)*(5/7) = 2275 cm cube.

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