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प्रश्न
A hemispherical bowl of internal radius 9 cm is full of liquid. This liquid is to be filled into conical shaped small containers each of diameter 3 cm and height 4 cm. How many containers are necessary to empty the bowl?
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उत्तर
Radius of hemispherical bowl = 9 cm
Volume = `1/2 xx 4/3pir^3`
= `2/3pi9^3`
= `2/3pi xx 729`
= 486π cm3
Diameter each of cylindrical bottle = 3 cm
Radius = `3/2` cm and height = 4 cm
∴ Volume of bottle = `1/3pir^2h`
= `1/3pi xx (3/2)^2 xx 4`
= 3π
∴ No. of bottles = `(486pi)/(3pi) = 162`
संबंधित प्रश्न
Find the surface area of a sphere of diameter 21 cm.
`["Assume "pi=22/7]`
A right circular cylinder just encloses a sphere of radius r (see figure). Find
- surface area of the sphere,
- curved surface area of the cylinder,
- ratio of the areas obtained in (i) and (ii).
Assuming the earth to be a sphere of radius 6370 km, how many square kilo metres is area
of the land, if three-fourth of the earth’s surface is covered by water?
A cylinder of same height and radius is placed on the top of a hemisphere. Find the curved
surface area of the shape if the length of the shape be 7 cm.
A solid is in the form of a cone standing on a hemi-sphere with both their radii being equal to 8 cm and the height of cone is equal to its radius. Find, in terms of π, the volume of the solid.
Find the surface area and volume of sphere of the following radius. (π = 3.14 )
3.5 cm
The internal and external diameters of a hollow hemi-spherical vessel are 21 cm and 28 cm respectively. Find volume of material of the vessel.
A solid, consisting of a right circular cone standing on a hemisphere, is placed upright, in a right circular cylinder, full of water and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of the hemisphere is 2 cm and the height of the cone is 4 cm. Give your answer to the nearest cubic centimetre.
The radius of two spheres are in the ratio of 1 : 3. Find the ratio between their volume.
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`)
