Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the surface area of a sphere of radius 5.6 cm.
`["Assume "pi=22/7]`
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 wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base
of the cone is 16 cm and its height is 15 cm. Find the cost of painting the toy at Rs. 7 per 100
`cm^2`.
The surface area of a sphere is 2464 cm2, find its volume.
The volume of a sphere is 38808 cm3; find its diameter and the surface area.
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.
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]
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.
A hemispherical and a conical hole is scooped out of a.solid wooden cylinder. Find the volume of the remaining solid where the measurements are as follows:
The height of the solid cylinder is 7 cm, radius of each of hemisphere, cone and cylinder is 3 cm. Height of cone is 3 cm.
Give your answer correct to the nearest whole number.Taken`pi = 22/7`.
