Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
A solid cube of side 2a has surface area 24a^2. What is the total surface area of all the pieces after n symmetrical cuts?
A cube of side 2a has surface area 24a^2. When it is cut parallel to a surface, through the centre, two cuboids of sides 2a, 2a and a are formed. The total surface area of one of these cuboids is 4(2a*a) + 2(2a*2a) = 16a^2. Therefore the total of both pieces is 32a^2. When these cuboids are cut again, symmetrically, the area increases to 40a^2.
No. of cuts Area/a^2
0 24
1 32
2 40
.... .....
n T(n)
Is this an A.P. with common difference 8?
Can you prove it?
1 Answer
- ViolaLv 57 years agoFavorite Answer
Yes, because each cut exposes an extra two 4a² square faces, i.e. 8a² each time.