Question

the ratio of the areas of two similar prisms is 49:81 what is the ratio of their volumes?

Answer 1

Answer:

Step-by-step explanation:

Ratio of area 49ratio 81

Ratio of sides 7 ratio 9

Ratio of volume 343 ratio 729

Answer 2

Given:

The ratio of the areas of two similar prisms is 49 : 81

Find:

We have to find ratio of their volumes

Solution:

Let the sides of first prism is a, b, and c then we have given second prism is similar to this one that means the proportional sides will be ka, kb, and kc

Then

$\frac{SA1}{SA2} =\frac{49}{81} \\\frac{2(ab+bc+ca)}{2(kakb+kbkc+kcka)} =\frac{49}{81} \\\\\frac{1}{k^2} =\frac{49}{81} \\k=\frac{9}{7}$

So the volume ratio will be

$\frac{V1}{V2} =\frac{abc}{ka.kb.kc} \\ =\frac{1}{k^3} \\ =\frac{343}{729}$

This is the required answer.