Advertisements
Advertisements
प्रश्न
A spherical ball of lead has been melted and made into identical smaller balls with radius equal to half the radius of the original one. How many such balls can be made?
Advertisements
उत्तर
Let the radius of spherical ball = r
∴ Volume = `4/3pir^3`
Radius of smaller ball = `r/2`
∴ Volume of smaller ball = `4/3pi(r/2)^3`
= `4/3pir^3/8`
= `(pir^3)/6`
Therefore, number of smaller balls made out of the given ball
= `(4/3pir^3)/((pir^3)/6)`
= `4/3 xx 6`
= 8
APPEARS IN
संबंधित प्रश्न
A right circular cylinder just encloses a sphere of radius r (see figure). Find
- surface area of the sphere,
- curved surface area of the cylinder,
- ratio of the areas obtained in (i) and (ii).
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.
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.
Eight metallic spheres; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere.
The total surface area of a hemisphere of radius r is
If the surface area of a sphere is 2826 cm2 then find its volume. ( π= 3.14)
Find the radius of the sphere whose surface area is equal to its volume .
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?
The internal and external diameters of a hollow hemispherical vessel are 20 cm and 28 cm respectively. Find the cost to paint the vessel all over at ₹ 0.14 per cm2
