Answered

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?

Verified Answer :

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 \(5\ m\)

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

\(z^{3}=\frac{125}{27}\\ \\z=\sqrt[3]{\frac{125}{27}}\\ \\z=\frac{5}{3}\)

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

\(\frac{5}{3}(3)=5\ m\)


Related Questions