Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Side (a) of cube = 12 cm
Volume of cube = (a)3 = (12 cm)3 = 1728 cm3
Let the side of the smaller cube be a1.
`"Volume of 1 smaller cube "=(1728/8)cm^3=216cm^3`
(a1)3 = 216 cm3
⇒ a1 = 6 cm
Therefore, the side of the smaller cubes will be 6 cm.
`"Ratio between surface areas of cubes "="Surface area of bigger cube"/"Surface area of smaller cube"`
`=(6a^2)/(6a_1^2) = 12^2/6^2 = 4/1`
Therefore, the ratio between the surface areas of these cubes is 4:1.
संबंधित प्रश्न
If the area of three adjacent faces of a cuboid are 8 `cm^2`, 18 `cm^3` and 25 `cm^3`. Find the
volume of the cuboid.
How many cubic centimeters of iron are there in an open box whose external dimensions are 36 cm, 25 cm and I 6.5 cm, the iron being 1.5 cm thick throughout? If I cubic cm of iron weighs 15g, find the weight of the empty box in kg.
A rectangular tank is 80 m long and 25 m broad. Water flows into it through a pipe whose cross-section is 25 cm2, at the rate of 16 km per hour. How much the level of the water rises in the tank in 45 minutes.
The dimensions of a match box are 6 cm × 3.5 cm × 2.5 cm. Find the volume of a packet containing 12 such match boxes
The length, breadth and depth of a pond are 20.5 m, 16 m and 8 m respectively. Find the capacity of the pond in litres
The dimensions of a brick are 24 cm × 12 cm × 8 cm. How many such bricks will be required to build a wall of 20 m length, 48 cm breadth and 6 m height?
A metallic cube with side 15 cm is melted and formed into a cuboid. If the length and height of the cuboid is 25 cm and 9 cm respectively then find the breadth of the cuboid
The volume of a cuboid is 660 cm3 and the area of the base is 33 cm2. Its height is
A swimming pool is 200 m by 50 m and has an average depth of 2 m. By the end of a summer day, the water level drops by 2 cm. How many cubic metres of water is lost on the day?
A birthday cake has two tiers as shown in the figure below. Find the volume of the cake.
 |
 |
