Advertisements
Advertisements
प्रश्न
The total area of a solid metallic sphere is 1256 cm2. It is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate :
- the radius of the solid sphere.
- the number of cones recast. [Take π = 3.14]
Advertisements
उत्तर
Total area of solid metallic sphere = 1256 cm2
i. Let radius of the sphere is r then
4πr2 = 1256
`=> 4 xx 22/7r^2 = 1256`
`=> r^2 = (1256 xx 7)/(4 xx 22)`
`=> r^2 = (157 xx 7)/11`
`=> r^2 = 1099/11`
`=> r = 1099/11`
`=> r = sqrt(99.909) = 9.995 cm`
`=>` r = 10 cm
ii. Volume of sphere = `4/3pir^3`
= `4/3 xx 22/7 xx 10 xx 10 xx 10`
= `88000/21 cm^3`
Volume of right circular cone = `1/3pir^2h`
= `1/3 xx 22/7 xx (2.5)^2 xx 8`
= `1100/21 cm^3`
Number of cones
= `88000/21 ÷ 1100/21`
= `88000/21 xx 21/1100`
= 80
APPEARS IN
संबंधित प्रश्न
A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of ₹ 16 per 100 cm2.
`["Assume "pi=22/7]`
The surface area of a sphere is 5544 `cm^2`, find its diameter.
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.
Spherical marbles of diameter 1.4 cm are dropped into beaker containing some water and are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm.
What is the least number of solid metallic spheres, each of 6 cm diameter, that should be melted and recast to form a solid metal cone whose height is 45 cm and diameter 12 cm?
The ratio between the volume of a sphere and volume of a circumscribing right circular cylinder is
A solid metallic cylinder has a radius of 2 cm and is 45 cm tall. Find the number of metallic spheres of diameter 6 cm that can be made by recasting this cylinder .
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)`
The volume of a sphere is 905 1/7 cm3, find its diameter.
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.
