Ash R.

asked • 01/11/15

the masses of two similar objects are 24kg and 81 kg respectively. if the surface area of the larger object is 540 cm^2, find the surface area of the smaller ob

Geometry of o levels

Philip P.

The important thing for you to remember, Ash, is that for two similar figures A and B:
  • (Length of a side A) / (Length of corresponding side B) = scale factor
  • (Area A) / (Area B) = (scale factor)2
  • (Volume A) / (Volume B) = (scale factor)3
Report

01/11/15

1 Expert Answer

By:

Philip P. answered • 01/11/15

Tutor
4.9 (484)

Affordable, Experienced, and Patient Geometry Tutor

See tutors like this
See tutors like this
Since the objects are similar, they have the same density.  The mass is density times volume.  So:
 
(mass smaller) / (mass larger) = (scale factor)3
 
(24 kg) / (81 kg) = (scale factor)3
 
(23*3 kg) / (33*3 kg) = (scale factor)3
 
2/3 = scale factor
 
(surface area smaller) / (surface area larger) = (scale factor)2
 
(surface area smaller) = (surface area larger) * (scale factor)2
 
Can you finish it from here?
Upvote • 1 Downvote
More
Report

Ash R.

sir i cud,nt understand this step
 

(23*3 kg) / (33*3 kg) = (scale factor)3

2/3 = scale factor
Report

01/11/15

Ash R.

sir here we will take mass of smaller/mass of larger. can we not take mass of larger / smaller
Report

01/11/15

Philip P.

24 = 8*3 = 23 *3        (23 = 2*2*2 = 8)
 
81 = 27*3 = 33 *3      (33 = 3*3*3 = 27)
 
For the scale factor, you can take the ratio either way: larger/smaller or smaller/larger.  Since you are given the larger mass, it's simpler to use the smaller/larger scale factor; but either will work.
Report

01/11/15

Ash R.

thanx sir. this helped me a lot
Report

01/12/15

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.