Advertisements
Advertisements
प्रश्न
A manufacturing company prepares spherical ball bearings, each of radius 7 mm and mass 4 gm. These ball bearings are packed into boxes. Each box can have a maximum of 2156 cm3 of ball bearings. Find the:
- maximum number of ball bearings that each box can have.
- mass of each box of ball bearings in kg.
(Use π = `22/7`)
Advertisements
उत्तर
Given: Radius = 7 mm = 0.7 cm = `7/10` cm ....(since 1 cm = 10 mm)
Volume of bearings per box = 2156 cm3
Mass of one bearing = 4 g
π = `22/7`
a. Maximum number of ball bearings:
Volume of one ball = `4/3πr^3`
= `4/3 xx 22/7 xx (7/10)^3`
No. of balls = `2156/(4/3 xx 22/7 xx (7/10)^3)`
= `(2156 xx 3 xx 10^3)/(4 xx 22 xx 7^2)`
= `(2156 xx 3000)/(4312)`
= 1500
b. Mass of each box of ball bearings:
Total mass = 1500 × 4 g
= 6000 g
= 6 kg
संबंधित प्रश्न
A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast.
Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm. Find the radius of the base of each smaller cone, if height of each is 108 cm.
A solid rectangular block of metal 49 cm by 44 cm by 18 cm is melted and formed into a solid sphere. Calculate the radius of the sphere.
Spherical marbles of diameter 1.4 cm are dropped into beaker containing some water and are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm.
A largest sphere is to be carved out of a right circular cylinder of radius 7 cm and height 14 cm. Find the volume of the sphere.
Find the total surface area of a hemisphere of radius 10 cm.
If the ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is
The surface area of a solid metallic sphere is 2464 cm2. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate : the number of cones recast. `("Take" pi =22/7)`
A sphere cut out from a side of 7 cm cubes. Find the volume of this sphere?
A vessel is in he form of an inverted cone. Its height is 11 cm., and the radius of its top which is open is 2.5 cm. It is filled with water up to the rim. When lead shots, each of which is a sphere of radius 0.25 cm., are dropped 2 into the vessel, `2/5`th of the water flows out. Find the number of lead shots dropped into the vessel.
