Advertisements
Advertisements
प्रश्न
A hollow sphere of internal and external diameter 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.
Advertisements
उत्तर
External diameter = 8 cm
Therefore, radius (R) = 4 cm
Internal diameter = 4 cm
Therefore, radius (r) = 2 cm
Volume of metal used in hollow sphere = `4/3pi(R^3 - r^3)`
= `4/3 xx 22/7 xx (4^3 - 2^3)`
= `88/21(64 - 8)`
= `88/21 xx 56 cm^3` ...(i)
Diameter of cone = 8 cm
Therefore, radius = 4 cm
Let height of cone = h
∴ Volume = `1/3pir^2h`
= `1/3 xx 22/7 xx 4 xx 4 xx h`
= `352/21 h` ...(ii)
From (i) and (ii)
`352/21 h = 88/21 xx 56`
`=> h = (88 xx 56 xx 21)/(21 xx 352) = 14 cm`
Height of the cone = 14 cm.
संबंधित प्रश्न
A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and recast into small cones of base radius 2 cm and height 8 cm. Find the number of cones.
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.
Mark the correct alternative in each of the following:
In a sphere the number of faces is
The model of a building is constructed with the scale factor 1 : 30.
(i) If the height of the model is 80 cm, find the actual height of the building in meters.
(ii) If the actual volume of a tank at the top of the building is 27m3, find the volume of the tank on the top of the model.
Find the surface area of a sphere, if its volume is 38808 cubic cm. `(π = 22/7)`
From a rectangular solid of metal 42 cm by 30 cm by 20 cm, a conical cavity of diameter 14 cm and depth 24 cm is drilled out. Find: the weight of the material drilled out if it weighs 7 gm per cm3.
The volume of a sphere is 905 1/7 cm3, find its diameter.
A sphere cut out from a side of 7 cm cubes. Find the volume of this sphere?
The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is ______.
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`)
