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Two pyramids are similar with a ratio of surface areas of 25:36. Find the volume of the larger pyramid given that the first has a volume of 250m3.

Respuesta :

Answer:

432m^3

Step-by-step explanation:

The computation of the volume of the larger pyramid is shown below:

Let us assume the volume of the larger pyramid be x

Given that

The ratio of two pyramids is 25:36

We can say that

The Ratio of side = (The ratio of surface area)^[tex]\frac{1}{2}[/tex] = [tex]\frac{5}{6}[/tex]

Now

ratio of volume = (ratio of side)^3 =  [tex]\frac{5^{3}}{6^{3}}[/tex] = 125 : 216

Based on the above information, the calculation is as follows

[tex]\frac{125}{216} = \frac{250}{x}[/tex]

So,

[tex]x = \frac{250 \times 216}{125}[/tex]

= 432m^3

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