Advertisements
Advertisements
प्रश्न
If V is the volume of a cuboid of dimensions a, b, c and S is its surface area, then prove that
`1/V=2/S(1/a+1/b+1)`
Advertisements
उत्तर
Given that
Length = a
Breadth = b
Height = c
Volume `(v)=lxxbxxh`
`=axxbxxc=abc`
Surface area `2(lb+bh+hl)`
`=2(ab+bc+ac)`
`Now , 2/5[1/a+1/b+1/c]=2/(2(ab+bc+ca)) [[ab+bc+ca]]/(abc)`
`1/(abc)=1/v`
APPEARS IN
संबंधित प्रश्न
Given that 1 cubic cm of marble weighs 0.25 kg, the weight of marble block 28 cm in width and 5 cm thick is 112 kg. Find the length of the block.
The external dimensions of a closed wooden box are 48 cm, 36 cm, 30 cm. The box is made of 1.5 cm thick wood. How many bricks of size 6 cm x 3 cm x 0.75 cm can be put in this box?
A field is in the form of a rectangle of length 18 m and width 15 m. A pit, 7.5 m long, 6 m broad and 0.8 m deep, is dug in a corner of the field and the earth taken out is spread over the remaining area of the field. Find out the extent to which the level of the field has been raised.
Volume of a cuboid is 34.50 cubic metre. Breadth and height of the cuboid is 1.5m and 1.15m respectively. Find its length.
To make an open fish tank, a glass sheet of 2 mm gauge is used. The outer length, breadth and height of the tank are 60.4 cm, 40.4 cm and 40.2 cm respectively. How much maximum volume of water will be contained in it?
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 ______.
A covered wooden box has the inner measures as 115 cm, 75 cm and 35 cm and thickness of wood as 2.5 cm. The volume of the wood is ______.
A carpenter makes a box which has a volume of 13,400 cm3. The base has an area of 670 cm2. What is the height of the box?
Water flows from a tank with a rectangular base measuring 80 cm by 70 cm into another tank with a square base of side 60 cm. If the water in the first tank is 45 cm deep, how deep will it be in the second tank?
