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
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).
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 radius of the sphere.
- the number of cones recast. (Take π = `22/7`)
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 total surface area of a hemisphere and a solid hemisphere each of radius 10 cm.
(Use 𝜋 = 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.
The surface area of a sphere is 2464 cm2, find its volume.
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 volume of a sphere whose surface area is 154 cm2.
If a sphere is inscribed in a cube, find the ratio of the volume of cube to the volume of the sphere.
The ratio of the total surface area of a sphere and a hemisphere of same radius is
If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of the cube is
If the radius of a solid hemisphere is 5 cm, then find its curved surface area and total surface area. ( π = 3.14 )
Find the surface area of a sphere, if its volume is 38808 cubic cm. `(π = 22/7)`
Find the length of the wire of diameter 4 m that can be drawn from a solid sphere of radius 9 m.
The internal and external diameters of a hollow hemi-spherical vessel are 21 cm and 28 cm respectively. Find volume of material of the vessel.
There is a ratio 1: 4 between the surface area of two spheres, find the ratio between their radius.
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 hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is ______.
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`)
