Advertisements
Advertisements
प्रश्न
If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball (in sq.cm) is
विकल्प
100 π
75 π
60 π
50 π
Advertisements
उत्तर
In the given problem, Let the radius of smaller spherical balls which can be made from a bigger ball be xunits.
Here,
The radius of the bigger ball (r1) = 10 cm
The radius of the smaller ball (r2) = x cm
The number of smaller balls = 8
So, volume of the big ball is equal to the volume of 8 small balls.
Volume of the big balls = volume of the 8 small balls
`(4/3)pi r_1^3 = 8 (4/3) pi x^3`
`(4/3) pi (10)^3 =8 (4/3) pi x^3`
`(10)^3 = 8 x^3`
`x^3 = 1000/8`
Further, solving for x, we get,
`x=3sqrt(1000/8) `
`x = 10/2`
x = 5
Now, surface area of a small ball of radius 5 cm = `4 pi r^2`
`= 4 pi(5)^2`
`= 100 pi`
Therefore, the surface area of the small spherical ball is `100 pi`.
APPEARS IN
संबंधित प्रश्न
Find the surface area of a sphere of diameter 3.5 m.
`["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.
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.
Find the surface area of a sphere of diameter 14 cm.
Find the total surface area of a hemisphere and a solid hemisphere each of radius 10 cm.
(Use 𝜋 = 3.14)
A cylinder of same height and radius is placed on the top of a hemisphere. Find the curved
surface area of the shape if the length of the shape be 7 cm.
A hemi-spherical dome of a building needs to be painted. If the circumference of the base of
the dome is 17.6 cm, find the cost of painting it, given the cost of painting is Rs. 5 per l00
`cm^2`
The volume of a sphere is 38808 cm3; find its diameter and the surface area.
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.
Spherical marbles of diameter 1.4 cm are dropped into beaker containing some water and are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm.
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.
The hollow sphere, in which the circus motor cyclist performs his stunts, has a diameter of 7 m. Find the area available to the motorcyclist for riding.
If a sphere of radius 2r has the same volume as that of a cone with circular base of radius r, then find the height of the cone.
If a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of the cone 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 )
9 cm
If the radius of a solid hemisphere is 5 cm, then find its curved surface area and total surface area. ( π = 3.14 )
How many lead balls of radii 1 cm each can be made from a sphere of 8 cm radius?
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 number of cones recasted [π = 3.14]
From a rectangular solid of metal 42 cm by 30 cm by 20 cm, a conical cavity of diameter 14 cm and depth 24 cm is drilled out. Find: the weight of the material drilled out if it weighs 7 gm per cm3.
