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
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.
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 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.
Find the surface area of a sphere of radius 14 cm.
Find the surface area of a sphere of diameter 3.5 cm.
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 wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base
of the cone is 16 cm and its height is 15 cm. Find the cost of painting the toy at Rs. 7 per 100
`cm^2`.
If the number of square centimeters on the surface of a sphere is equal to the number of cubic centimeters in its volume, what is the diameter of the sphere?
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 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.
A hemi-spherical bowl has negligible thickness and the length of its circumference is 198 cm. Find the capacity of the bowl.
Find the radius of a sphere whose surface area is 154 cm2.
If a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of the cone is
A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder. If the radius of the sphere is r, then the volume of the cylinder is
A cone and a hemisphere have equal bases and equal volumes the ratio of their heights is
Find the volume and surface area of a sphere of diameter 21 cm.
