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
A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold? (1 m3 = 1000l)
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.
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 village having a population of 4000 requires 150 litres of water per head per day. It has a tank measuring 20 m × 15 m × 6 m. For how many days will the water of this tank last?
Volume of regular solids such as cube and cuboid can be found by multiplying the dimensions. Complete the given table by finding the volume of the given objects
| S.No. | Objects | l | b | h | Volume (cubic cm) |
| 1. | Note books | 6 cm | 15 cm | 1 cm | |
| 2. | Name board | 20 cm | 90 cm | 2 cm | |
| 3. | Show case cub board | 70 cm | 250 cm | 70 cm | |
| 4. | Gift box | 10 cm | 10 cm | 10 cm | |
| 5. | Dice | 1 cm | 1 cm | 1 cm |
A storage tank is in the form of a cube. When it is full of water, the volume of water is 15.625 m3. If the present depth of water is 1.3 m, find the volume of water already used from the tank.
The surface area of the three coterminus faces of a cuboid are 6, 15 and 10 cm2 respectively. The volume of the cuboid is ______.
Ramesh has three containers.
- Cylindrical container A having radius r and height h,
- Cylindrical container B having radius 2r and height 1/2 h, and
- Cuboidal container C having dimensions r × r × h
The arrangement of the containers in the increasing order of their volumes 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?
