Advertisements
Advertisements
प्रश्न
A cube of side 5 cm is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the original cube to that of the sum of the surface areas of the smaller cubes?
Advertisements
उत्तर
Surface area of a cube = 6a2, where a is side of a cube.
... Side of cube = 5 cm
... Surface area of the cube = 6 × (5)2 = 6 × 25 = 150 cm2
Now, surface area of the cube with side 1 cm = 6 × (1)2 = 6 cm2
... Surface area of 5 cubes with side 1 cm = 5 × 6 = 30 cm2
Ratio of the surface area of the original cube to that of the sum of the surface area of the smaller cubes
= `30/150`
= `3/15`
= 1 : 5
APPEARS IN
संबंधित प्रश्न
Find the volume of a cube whose side is 25 mm .
Fill in the blank in the following so as to make the statement true:
1 kl = ....... m3
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.
Two cubes, each of volume 512 cm3 are joined end to end. Find the surface area of the resulting cuboid.
The square on the diagonal of a cube has an area of 1875 sq. cm. Calculate:
(i) The side of the cube.
(ii) The total surface area of the cube.
The edges of three cubes of metal are 3 cm, 4 cm, and 5 cm. They are melted and formed into a single cube. Find the edge of the new cube.
The dimensions of a rectangular box are in the ratio 4: 2 : 3. The difference between the cost of covering it with paper at Rs. 12 per m2 and with paper at the rate of 13.50 per m2 is Rs. 1,248. Find the dimensions of the box.
The length of the diagonals of a cube is 8√3 cm.
Find its:
(i) edge
(ii) total surface area
(iii) Volume
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 base of a rectangular container is a square of side 12 cm. This container holds water up to 2 cm from the top. When a cube is placed in the water and is completely submerged, the water rises to the top and 224 cm3 of water overflows. Find the volume and surface area of the cube.
