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/c]`
उत्तर
The volume (V) of a cuboid = a x b x c
`:. 1/V = 1/(abc)` .......(1)
The surface area (S) of a cuboid = 2(ab + bc + ca) .....(2)
`2/S = 1/(ab+bc+ac)`
RHS = `2/S (1/a + 1/b + 1/c)= 1/(ab +bc+ac)(1/a+1/b+1/c)`
`2/S xx (1/a+1/b+1/c) = 1/(abc)`
`:. 2/S xx(1/a+ 1/b + 1/c)= 1/V`
APPEARS IN
संबंधित प्रश्न
Find the surface area of a sphere of radius 4.2 cm. (π = `22/7`)
Find the diagonal of a square whose side is 10 cm.
The volume of a cube is 1000 cm3. Find the side of a cube.
Find the volume and surface area of a sphere of radius 2.1 cm. `(pi=22/7)`
The volume of a cube is 512 cm3. Find its side.
The volume of a cube is 343 cm3. Find its total surface area.
As shown in the figure, a cylindrical glass contains water. A metal sphere of diameter 2 cm is immersed in it. Find the volume of the water.
The diameter and thickness of a hollow metals sphere are 12 cm and 0.01 m respectively. The density of the metal is 8.88 gm per cm3. Find the outer surface area and mass of the sphere.
Find the curved surface area of a sphere of radius 1cm. (π = 3.14)
Find the volume and surface area of a sphere of radius 8.4 cm.
`(pi=22/7)`
The dimensions of a cuboid in cm are 30 × 18 × 10. Find its volume.
The volume of a cube is 1000 cm3. Find its total surface area.
The length, breadth, and height of a cuboid are in the ratio 5:4: 2. If the total surface area is 1216 cm2, find dimensions of the solid.
Find the volume of a cube of side 3 cm ______.
Water is flowing at the rate of 15 km/h through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm?
What should be the speed of water if the rise in water level is to be attained in 1 hour?
A cylinder of radius 12 cm contains water up to the height 20 cm. A spherical iron ball is dropped into the cylinder and thus water level raised by 6.75 cm. What is the radius of iron ball?
