Advertisements
Advertisements
प्रश्न
The cylinder of radius 12 cm have filled the 20 cm with water. One piece of iron drop in the stands of water goes up 6.75 cm. Find the radius of sphere piece.
उत्तर
Radius of cylinder = 12 cm
Height of cylinder = 6.75 cm
Volume of water = πr2h = π x 12 x 12 x 6.75 cm3
Let the radius of iron sphere piece = R cm.
∵ Volume of sphere = volume of water
`4/3` πR3 = π x 12 x 12 x 6.75
R3 = `(π xx 12 xx 12 xx 6.75 xx 3)/(4π)`
R3 = 729
R = `root(3)(729)` = 9 cm.
Hence radius of sphere piece = 9 cm.
APPEARS IN
संबंधित प्रश्न
Find the surface area of a sphere of diameter 14 cm.
`["Assume "pi=22/7]`
On a map drawn to a scale of 1: 50,000, a rectangular plot of land ABCD has the following dimensions. AB = 6 cm; BC = 8 cm and all angles are right angles. Find:
1) the actual length of the diagonal distance AC of the plot in km.
2) the actual area of the plot in sq. km.
How many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 cm?
The surface area of a solid sphere is increased by 12% without changing its shape. Find the percentage increase in its:
- radius
- volume
Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r cm.
The ratio of the total surface area of a sphere and a hemisphere of same radius is
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
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 and volume of sphere of the following radius. (π = 3.14 )
3.5 cm
The radius of a sphere is 9 cm. It is melted and drawn into a wire of diameter 2 mm. Find the length of the wire in metre.
Find the length of the wire of diameter 4 m that can be drawn from a solid sphere of radius 9 m.
A sphere has the same curved surface area as the curved surface area of a cone of height 36 cm and base radius 15 cm . Find the radius of the sphere .
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 .
A solid, consisting of a right circular cone standing on a hemisphere, is placed upright, in a right circular cylinder, full of water and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of the hemisphere is 2 cm and the height of the cone is 4 cm. Give your answer to the nearest cubic centimetre.
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?
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.
The total surface area of a hemisphere is how many times the square of its radius
