A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.
A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.
Side of a cube = 12cm (Given)
Find the volume of cube:
Volume of cube = (Side)3
= (12)3cm3
= 1728cm3
Surface area of a cube with side 12 cm = 6a2
= 6(12) 2 cm2 ….........(1)
Cube is cut into eight small cubes of equal volume, say side of each cube is p.
Volume of a small cube = p3
Surface area = 6p2 …...........(2)
Volume of each small cube = (1728/8) cm3
= 216 cm3
(p)3 = 216 cm3
p = 6 cm
Now, Surface areas of the cubes ratios = (Surface area of bigger cube)/(Surface area of smaller cubes)
From equation (1) and (2), we get
Surface areas of the cubes ratios = (6a2)/(6p2)
= a2/p2 = 122/62
= 4
Therefore, the required ratio is 4 : 1.
-
The diameter of a sphere is decreased by 25%. By what percent does its curved surface area decrease?
3 years ago
-
The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in fig. Eight such spheres are used forth is purpose, and are to be painted silver.
3 years ago
-
A wooden bookshelf has external dimensions as follows: Height = 110cm, Depth = 25cm, Breadth = 85 cm (see fig.). The thickness of the plank is 5cm everywhere.
3 years ago
-
A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm^3) is needed to fill this capsule?
3 years ago
-
Twenty-seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S’.
3 years ago
- 321 Forums
- 27.3 K Topics
- 53.8 K Posts
- 0 Online
- 12.4 K Members