Advertisements
Advertisements
Question
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.
Advertisements
Solution
Radius of sphere = 9 cm
Volume of sphere = `4/3pir^3`
= `4/3 xx 22/7 xx 9 xx 9 xx 9`
= `3054.857 "cm"^3 = 30.55 xx 10^-4 "m"^3` .....(i)
Diameter of cylindrical wire = 2 mm
Therefore, radius = 1 mm = 0.001 m
Let length of wire be h
∴ Volume = `pir^2h`
= `22/7 xx 0.001 xx 0.001 xx h`
= `3.142h xx 10^-6` m3 ....................(ii)
From (i) and (ii)
⇒ `3.142 xx 10^-6h = 30.55 xx 10^-4`
⇒ `h = (30.55 xx 10^-4)/(3.142 xx 10^-6)`
⇒ h = 972m
Length of the wire = 972 m
RELATED QUESTIONS
Find the surface area of a sphere of radius 5.6 cm.
`["Assume "pi=22/7]`
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.
If the surface area of a sphere is 144π m2, then its volume (in m3) is
The ratio between the volume of a sphere and volume of a circumscribing right circular cylinder is
Find the volume of a sphere, if its surface area is 154 sq.cm.
Find the length of the wire of diameter 4 m that can be drawn from a solid sphere of radius 9 m.
A hemispherical bowl of internal radius 9 cm is full of liquid. This liquid is to be filled into conical shaped small containers each of diameter 3 cm and height 4 cm. How many containers are necessary to empty the bowl?
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.
Find the volume and surface area of a sphere of diameter 21 cm.
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?
