Advertisements
Advertisements
प्रश्न
If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively melted into a cone of base diameter 8 cm, then find the height of the cone.
Advertisements
उत्तर
In the given problem, we have a hollow sphere of given dimensions;
Internal diameter of the sphere (d) = 4 cm
External diameter of the sphere (D) = 8 cm
Now, the given sphere is molded into a cone,
Diameter of the base of cone (dc) = 8 cm
Now, the volume of hollow sphere is equal to the volume of the cone.
So, let the height of cone = h cm
Therefore, we get
Volume of cone = the volume of hollow sphere
`(1/3) pi ((d_c)/2)^2 h = (4/3) pi ((D/2)^3 -(d/2)^3)`
`(1/3) pi (8/2)^2 (h) = (4/3) pi ((8/2)^3 -(4/2)^3)`
`(1/3)pi (4)^2 (h) = (4/3) pi (64-8)`
Further, solving for h,
` h = ((4/3) pi (56))/((1/3) pi (16))`
`h = ((4)(56))/((16))`
h = 14 cm
So, height of the cone is 14 cm
APPEARS IN
संबंधित प्रश्न
Find the radius of a sphere whose surface area is 154 cm2.
`["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 model of a ship is made to a scale 1: 300
1) The length of the model of the ship is 2 m. Calculate the lengths of the ship.
2) The area of the deck ship is 180,000 m2. Calculate the area of the deck of the model.
3) The volume of the model in 6.5 m3. Calculate the volume of the ship.
Two solid spheres of radii 2 cm and 4 cm are melted and recast into a cone of height 8 cm. Find the radius of the cone so formed.
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 surface area of a sphere of radius 14 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?
Eight metallic spheres; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere.
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.
Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm. Find the radius of the base of each smaller cone, if height of each is 108 cm.
A largest sphere is to be carved out of a right circular cylinder of radius 7 cm and height 14 cm. Find the volume of the sphere.
The cross-section of a tunnel is a square of side 7 m surmounted by a semi-circle as shown in the adjoining figure. The tunnel is 80 m long.
Calculate:
- its volume,
- the surface area of the tunnel (excluding the floor) and
- its floor area.
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.
A sphere and a cube are of the same height. The ratio of their volumes is
If the surface area of a sphere is 144π m2, then its volume (in m3) is
Find the surface area and volume of sphere of the following radius. (π = 3.14 )
9 cm
A vessel is in he form of an inverted cone. Its height is 11 cm., and the radius of its top which is open is 2.5 cm. It is filled with water up to the rim. When lead shots, each of which is a sphere of radius 0.25 cm., are dropped 2 into the vessel, `2/5`th of the water flows out. Find the number of lead shots dropped into the vessel.
The radius of a sphere increases by 25%. Find the percentage increase in its surface area
