Advertisements
Advertisements
प्रश्न
A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5 cm. Find the number of spheres formed.
Advertisements
उत्तर
A volume of solid cone = `1/3 pir^2h = 1/3 xx 22/7 xx 5^2 xx 8 = 1/3 xx 22/7 xx 25 xx 8`
Volume of a small sphere = `4/3 pir^3 = 4/3 xx 22/7 xx (5/10)^3 = 4/3 xx 22/7 xx 125/1000`
Number of spheres formed = `"Volumeof cone"/"Volumeof sphere"` = `(1/3 xx 22/7 xx 25xx8)/(4/3 xx 22/7 xx 125/1000) = 400`
Thus 400 spheres are obtained by melting the solid cone.
APPEARS IN
संबंधित 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`)
Find the surface area of a sphere of radius 5.6 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 surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height of the cone.
The largest sphere is cut off from a cube of side 6 cm. The volume of the sphere will be
A cone and a hemisphere have equal bases and equal volumes the ratio of their heights is
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`.
The given figure shows the cross-section of a cone, a cylinder and a hemisphere all with the same diameter 10 cm and the other dimensions are as shown.
Calculate :
- the total surface area.
- the total volume of the solid and
- the density of the material if its total weight is 1.7 kg.
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 surface area of a solid metallic sphere is 616 cm2. It is melted and recast into smaller spheres of diameter 3.5 cm. How many such spheres can be obtained?
