Advertisements
Advertisements
प्रश्न
If a sphere of radius 2r has the same volume as that of a cone with circular base of radius r, then find the height of the cone.
Advertisements
उत्तर
In the given problem, we are given a cone and a sphere which have equal volumes. The dimensions of the two are;
Radius of the cone (rc) = r
Radius of the sphere (rs) = 2r
Now, let the height of the cone = h
Here, Volume of the sphere = volume of the cone
`(4/3)pi r_s^3 = (1/3)pi r_c^2 h`
`(4/3)pi (2r)^3 = (1/3) pi (r)^2 h`
`(4/3) (8r^3)=(1/3)r^2 h`
Further, solving for h
`h = ((4)(8r^3))/((r^2))`
Therefore, the height of the cone is 32r.
APPEARS IN
संबंधित प्रश्न
Find the surface area of a sphere of radius 5.6 cm.
`["Assume "pi=22/7]`
The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.
The diameter of the moon is approximately one-fourth of the diameter of the earth. Find the ratio of their surface area.
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).
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.
How many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 cm?
Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted and recasted into a single solid sphere. Taking π = 3.1, find the surface area of the solid sphere formed.
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.
The total surface area of a hemisphere of radius r is
If the ratio of volumes of two spheres is 1 : 8, then the ratio of their surface areas is
A cone and a hemisphere have equal bases and equal volumes the ratio of their heights is
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is
Find the surface area and volume of sphere of the following radius. (π = 3.14)
4 cm
A solid metallic cylinder has a radius of 2 cm and is 45 cm tall. Find the number of metallic spheres of diameter 6 cm that can be made by recasting this cylinder .
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?
A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones used.
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.
A solid sphere is cut into two identical hemispheres.
Statement 1: The total volume of two hemispheres is equal to the volume of the original sphere.
Statement 2: The total surface area of two hemispheres together is equal to the surface area of the original sphere.
Which of the following is valid?
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`)
