Advertisements
Advertisements
प्रश्न
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`)
Advertisements
उत्तर
i. Total surface area of the sphere = 4πr2, where r is the radius of the sphere.
Thus,
4πr2 = 2464 cm2
`=> 4 xx 22/7 xx r^2 = 2464`
`=>` r2 = 196
`=>` r = 14 cm
∴ R = 14 cm
ii. Volume of sphere melted = `4/3 piR^3`
= `4/3 xx pi xx 14 xx 14 xx 14`
Radius of each cone recasted = r = 3.5 cm
Height of each cone recasted = h = 7 cm
∴ Volume of each cone recasted = `1/3 pir^2h`
= `1/3 xx pi xx 3.5 xx 3.5 xx 7`
∴ Number of cones recasted
= `"Volume of sphere melted"/"Volume of each cone formed"`
= `(4/3 xx pi xx 14 xx 14 xx 14)/(1/3 xx pi xx 3.5 xx 3.5 xx 7)`
= `(4 xx 14 xx 14 xx 14)/(3.5 xx 3.5 xx 7)`
= 4 × 4 × 4 × 2
= 128
APPEARS IN
संबंधित प्रश्न
A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.
`["Assume "pi = 22/7]`
Find the surface area of a sphere of radius 14 cm.
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.
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.
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 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 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.
If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of the cube is
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.
