Advertisements
Advertisements
Question
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.
Solution
Radius of a solid sphere = R = 15 cm
∴ Volume of sphere melted = `4/3piR^3`
= `4/3 xx pi xx 15 xx 15 xx 15`
Radius of each cone recasted = r = 2.5 cm
Height of each cone recasted = h = 8 cm
∴ Volume of each one cone recasted = `1/3pir^2h`
= `1/3 xx pi xx 2.5 xx 2.5 xx 8`
∴ Number of cones recasted = `"Volume of sphere melted"/"Volume of each cone formed"`
= `(4/3 xx pi xx 15 xx 15 xx 15)/(1/3 xx pi xx 2.5 xx 2.5 xx 8)`
= 270
RELATED QUESTIONS
Find the surface area of a sphere of radius 10.5 cm.
`["Assume "pi=22/7]`
Find the surface area of a sphere of radius 14 cm.
`["Assume "pi=22/7]`
The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.
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]`
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 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 surface area of a sphere of diameter 3.5 cm .
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.
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.
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]
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.
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.
How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter?
The largest sphere is cut off from a cube of side 6 cm. The volume of the sphere will be
Find the surface area and volume of sphere of the following radius. (π = 3.14 )
3.5 cm
Find the radius of a sphere whose surface area is equal to the area of the circle of diameter 2.8 cm
The radius of a sphere is 10 cm. If we increase the radius 5% then how many % will increase in volume?
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.
A solid sphere is cut into two identical hemispheres.
Statement 1: The total volume of two hemispheres is equal to the volume of the original sphere.
Statement 2: The total surface area of two hemispheres together is equal to the surface area of the original sphere.
Which of the following is valid?
