Advertisements
Advertisements
प्रश्न
Three metal cubes with edges 6 cm, 8 cm and 10 cm respectively are melted together and formed into a single cube. Find the volume, surface area and diagonal of the new cube.
Advertisements
उत्तर
Let the length of each edge of the new cube be a cm
Then,
`a^3=(6^3+8^3+10^3)cm^3`
`⇒ a^3= 1728`
`⇒ a = 12`
∴ Volume of new cube=`=a^3=1728cm^3`
Surface area of the new cube `6a^2=6xx12^2cm^2`
`= 864 cm^2`
Diagonals of the new cube = `sqrt(3a)= 12 sqrt3cm.`
APPEARS IN
संबंधित 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.
Water in a canal 30 cm wide and 12 cm deep, is flowing with a velocity of l00 km per hour.How much area will it irrigate in 30 minutes if 8 cm of standing water is desired?
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 cube of 9 cm edge is immersed completely in a rectangular vessel containing water. Ifthe dimensions of the base are 15 cm and 12 cm, find the rise in water level in the vessel.
A rectangular container, whose base is a square of side 5 cm, stands on a horizontal table, and holds water up to 1 cm from the top. When a cube is placed in the water it is completely submerged, the water rises to the top and 2 cubic cm of water overflows. Calculate the volume of the cube and also the length of its edge.
A field is 200 m long and 150 m broad. There is a plot, 50 m long and 40 m broad, near thefield. The plot is dug 7 m deep and the earth taken out is spread evenly on the field. Byhow many meters is the level of the field raised? Give the answer to the second place of decimal.
Complete the given table by finding the volume of the given objects.
| S.No. | Objects | l | b | h | Volume (cubic units) |
| 1. | Brick | 6 cm | 8 cm | 10 cm | — |
| 2. | Windowpane | 3 cm | — | 45 cm | 900 cubic cm |
| 3. | Sunshade | 70 cm | 20 cm | — | 4200 cubic cm |
| 4. | Steps | 80 cm | — | 20 cm | 32000 cubic cm |
| 5. | Room | — | 4 m | 3 m | 36 cubic m |
The surface area of the three coterminus faces of a cuboid are 6, 15 and 10 cm2 respectively. The volume of the cuboid is ______.
How many bricks of size 22 cm × 10 cm × 7 cm are required to construct a wall 11 m long, 3.5 m high and 40 cm thick, if the cement and sand used in the construction occupy (1/10)th part of the wall?
A birthday cake has two tiers as shown in the figure below. Find the volume of the cake.
 |
 |
