Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Find the total surface area of a hemisphere of radius 10 cm. [Use π = 3.14]
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).
Find the surface area of a sphere of diameter 21 cm.
Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm. Find the radius of the base of each smaller cone, if height of each is 108 cm.
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.
A cylindrical rod whose height is 8 times of its radius is melted and recast into spherical balls of same radius. The number of balls will be
Find the radius of a sphere whose surface area is equal to the area of the circle of diameter 2.8 cm
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.
The radius of a sphere is 10 cm. If we increase the radius 5% then how many % will increase in volume?
The radius of a sphere increases by 25%. Find the percentage increase in its surface area
