Question

geometry please help :)
Two similar solids are shown below.

Two similar solids are shown. The length of the smaller solid is 5 feet and its volume is 875 cubic feet. The length of the bigger solid is 7 feet. Its volume is not known.

What is the volume of the larger solid?

1750 ft3

1000 ft3

7000 ft3

3500 ft3

Answer 1

What is the ratio of the lengths (small to large).

Answer 2

?

Answer 3

im not sure what your asking. i just attached a picture

Answer 4

I am confused too. In the problem it says the length of the larger solid is 7feet. In the picture it shows a length of 10 feet. Which one is correct?

Answer 5

im sorry my fault. the question is, What is the volume of the larger solid? ignore the original post.

Answer 6

I'd defer to the picture, though it could be 2 valid exercises mixed up

Answer 7

my fault, the picture is correct

Answer 8

Okay, I am ignoring the original post. The ratio of the lengths of the small solid to the large solid is 5 to 10 or 5:10 = 1:2.

Answer 9

So the ratio of the lengths is 1:2. If I remember correctly my geometry textbook calls this the "scale factor".

Answer 10

or \(\bf \cfrac{10}{5} = \cfrac{v_2}{v_1}\)

Answer 11

What will the ratio of the volumes be?

Answer 12

incorrect.

Answer 13

@jdoe0001 you are close but not quite correct. The ratio of the volumes is not equal to 10:5 or 5:10.

Answer 14

to get the ratio of the volumes you must CUBE the ratio of the lengths.

Answer 15

ratio of volumes = (ratio of lengths)^3 = (1:2)^3 = 1:8

Answer 16

hmmm, that sounds right :)

Answer 17

\(\bf \cfrac{10^3}{5^3} = \cfrac{v_2}{v_1}\)

Answer 18

\[\frac{ 8 }{ 1 } = \frac{ v _{2} }{ v _{1} }\]

Answer 19

Yes, @jdoe0001, that it correct, however I present the same equation in simplified form.

Answer 20

indeed

Answer 21

so similar means in this case that all the lenghs are 2:1 ?

Answer 22

How's it going @LaurenAshley1201 ?

Answer 23

Yes @nistal.

Answer 24

@LaurenAshley1201
\[\frac{ 8 }{ 1 } = \frac{ v_{2} }{ 875 }\]

Answer 25

Cross multiply to find your volume for the larger solid. Ask me a question if this does not make sense.

Answer 26

>The length of the bigger solid is 7 feet. (posted)

On the diagram, the length is shown as 10.

So, I'm assuming the length of the second solid is 10.

I need to recalculate.

Answer 27

Theorem:

If two solids are similar, the cube of the scale factor of the two solids is equal to the ratio of the volumes.

(5/10)³ = 875/V where V is the volume of the larger solid

1/8 = 875/V

@LaurenAshley1201
Solve the equation for V.