The corresponding edges of two regular tetrahedrons are 1 cm and 3 cm. If the sum of the weights of the two tetrahedrons is 100 grams and both solids are made up of the same material, find the weight of the bigger solid.

Question

directrix · Answer

Any two regular tetrahedrons are similar. 

The cube of the scale factor is equal to the ratio of the volumes of the two similar solids.

directrix · Answer

That means:

(1/3)^3 = x/(100 - x) where x is the volume of the smaller solid

1/27  = x / (100 - x)

directrix · Answer

Cross multiply to get:

27*x = 100 - x

x = ?

Check my work

directrix · Answer

@saimon0926

directrix · Answer

@saimon0926

We are two steps away from an answer here if you will help me a bit.

anonymous · Answer

thank you :D

directrix · Answer

Okay, let's roll. Let me see where we were.

directrix · Answer

27*x = 100 - x
28x = 100
7x = 25
x = 25/7 ---> That's x but not the weight of the heavier solid.

directrix · Answer

100 - x = 100 - 25/7 = ?

If you don't like fractions (I do), you coud solve:

100 - 3.57 = ?

directrix · Answer

@saimon0926 

Just subtract 3.57 from 100 and that's the answer.

anonymous · Answer

it would be 96.4 right? :D thnx :D

directrix · Answer

Correct!

anonymous · Answer

thank you so much :)