Advertisements
Advertisements
प्रश्न
A solid cube of side 12 cm is cut into 8 identical cubes. What will be the side of the new cube? Also, find the ratio between the surface area of the original cube and the total surface area of all the small cubes formed.
Advertisements
उत्तर
Here, the cube of side 12 cm is divided into 8 cubes of side 9 cm.
Given that,
Their volumes are equal.
The volume of big cube of 12 cm = Volume of 8 cubes of side a cm
(Side of the big cube)3 = 8 x (Side of the small cube)3
(12)3 = 8 x a3
⇒ `a^3 = (12 xx 12 xx 12)/8`
⇒ `a^3 = 6^3` cm3
⇒ a = 6 cm
Ratio of their surface = `"Surface area of the original cube"/"Total surface area of the small cube"`
= `(6("side of big cube")^2)/(8 xx 6("side of small cube")^2)`
= `(6 xx 12 xx 12)/(8 xx 6 xx 6 xx 6) = 4/8 = 1:2`
So, the ratio is 1:2
APPEARS IN
संबंधित प्रश्न
Suppose that there are two cubes, having edges 2 cm and 4 cm, respectively. Find the volumes V1and V2 of the cubes and compare them.
Fill in the blank in the following so as to make the statement true:
The volume of a wooden cuboid of length 10 cm and breadth 8 cm is 4000 cm3. The height of the cuboid is ........ cm.
Three equal cubes are placed adjacently in a row. Find the ratio of total surface area of the new cuboid to that of the sum of the surface areas of the three cubes.
Three equal cubes are placed adjacently in a row. Find the ratio of the total surfaced area of the resulting cuboid to that of the sum of the total surface areas of the three cubes.
The ratio between the lengths of the edges of two cubes is in the ratio 3: 2. Find the ratio between their:
(i) total surface area
(ii) volume.
The length, breadth, and height of a cuboid are in the ratio 6: 5 : 3. If its total surface area is 504 cm2, find its volume.
Three metal cubes with edges 6cm, 8cm and 10cm respectively are melted together and formed into a single cube. Find the diagonal of this cube.
Three equal cubes are placed adjacently in a row. Find the ratio of the total surface area of the resulting cuboid to that of the sum of the total surface areas of the three cubes.
The volume of a cube is 64 cm3. Its surface area is ______.
A cube of side 3 cm painted on all its faces, when sliced into 1 cubic centimetre cubes, will have exactly 1 cube with none of its faces painted.
