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
Advertisements
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
Find the surface area of a sphere of radius 14 cm.
`["Assume "pi=22/7]`
Find the surface area of a sphere of diameter 14 cm.
`["Assume "pi=22/7]`
Find the total surface area of a hemisphere of radius 10 cm. [Use π = 3.14]
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.
Find the total surface area of a hemisphere and a solid hemisphere each of radius 10 cm.
(Use ЁЭЬЛ = 3.14)
The dome of a building is in the form of a hemisphere. Its radius is 63 dm. Find the cost of painting it at the rate of Rs. 2 per sq. m.
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.
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.
The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of the wire.
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.
Mark the correct alternative in each of the following:
In a sphere the number of faces is
The ratio between the volume of a sphere and volume of a circumscribing right circular cylinder 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 and volume of sphere of the following radius. (π = 3.14 )
3.5 cm
Find the volume of a sphere, if its surface area is 154 sq.cm.
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 volume of remaining solid
There is surface area and volume of a sphere equal, find the radius of sphere.
The radius of two spheres are in the ratio of 1 : 3. Find the ratio between their volume.
The surface area of a solid metallic sphere is 616 cm2. It is melted and recast into smaller spheres of diameter 3.5 cm. How many such spheres can be obtained?
