contestada

Two pyramids are similar. The volume of the larger pyramid is 125 m³ and the volume of the smaller pyramid is 27 m³. The height of the smaller pyramid is 3 m.

What is the height of the larger pyramid?

Respuesta :

scme1702
The volume is proportional to the cube of the height. Thus:

3³ : 27
h³ : 125

h = 5 m
calculista

Answer:

The height of the larger pyramid is [tex]5\ m[/tex]

Step-by-step explanation:

Step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> the scale factor

[tex]z^{3}=\frac{125}{27}\\ \\z=\sqrt[3]{\frac{125}{27}}\\ \\z=\frac{5}{3}[/tex]

Step 2

Find the height of the larger pyramid

we know that

To find the height of the larger pyramid multiply the scale factor by the height of the smaller pyramid

so

[tex]\frac{5}{3}(3)=5\ m[/tex]


Otras preguntas