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
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.
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`.
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 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 model of a building is constructed with the scale factor 1 : 30.
(i) If the height of the model is 80 cm, find the actual height of the building in meters.
(ii) If the actual volume of a tank at the top of the building is 27m3, find the volume of the tank on the top of the model.
Find the surface area of a sphere, if its volume is 38808 cubic cm. `(π = 22/7)`
Find the volume of a sphere, if its surface area is 154 sq.cm.
A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones used.
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?
