Advertisements
Advertisements
Question
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
Options
2r
3r
r
4r
Solution
In the given problem, we have a solid sphere which is remolded into a solid cone such that the radius of the sphere is equal to the height of the cone. We need to find the radius of the base of the cone.
Here, radius of the solid sphere (rs) = r cm
Height of the solid cone (h) = r cm
Let the radius of the base of cone (rc) = x cm
So, the volume of cone will be equal to the volume of the solid sphere.
Therefore, we get,
`(1/3) pi r_c^2 h = (4/3) pi r_s^3`
`(1/3) pi x^2 (r) = (4/3) pi (r)^3`
`x^2 = 4r^2`
` x = sqrt(4r^2)`
` x = 2r`
Therefore, radius of the base of the cone is 2r .
APPEARS IN
RELATED QUESTIONS
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 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.
The volume of one sphere is 27 times that of another sphere. Calculate the ratio of their :
- radii,
- surface areas.
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.
Find the surface area and volume of sphere of the following radius. (π = 3.14)
4 cm
Find the surface area and volume of sphere of the following radius. (π = 3.14 )
9 cm
Find the surface area of a sphere, if its volume is 38808 cubic cm. `(π = 22/7)`
The radius of a sphere is 9 cm. It is melted and drawn into a wire of diameter 2 mm. Find the length of the wire in metre.
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)`
How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter?
