Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Find the surface area of a sphere of diameter 14 cm.
`["Assume "pi=22/7]`
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 cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5 cm. Find the number of spheres formed.
A hemi-spherical dome of a building needs to be painted. If the circumference of the base of
the dome is 17.6 cm, find the cost of painting it, given the cost of painting is Rs. 5 per l00
`cm^2`
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 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.
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 volume of a sphere whose surface area is 154 cm2.
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.
If the surface area of a sphere is 2826 cm2 then find its volume. ( π= 3.14)
Find the volume of a sphere, if its surface area is 154 sq.cm.
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)`
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.
A sphere cut out from a side of 7 cm cubes. Find the volume of this sphere?
A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of the balls are 1.5 cm and 2 cm. Find the diameter of the third ball.
The radius of a sphere increases by 25%. Find the percentage increase in its surface area
The total surface area of a hemisphere is how many times the square of its radius
