Advertisements
Advertisements
Question
Eight metallic spheres; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere.
Advertisements
Solution
Radius of metallic sphere = `2 mm = 1/5 cm`
Volume = `4/3pir^3`
= `4/3 xx 22/7 xx 1/5 xx 1/5 xx 1/5`
= `88/(21 xx 125) cm^3`
Volume of 8 spheres = `(88 xx 8)/(21 xx 125)`
= `704/(21 xx 125) cm^3` ...(1)
Let radius of new sphere = R
∴ Volume = `4/3piR^3`
= `4/3 xx 22/7R^3`
= `88/21R^3` ...(2)
From (1) and (2)
`88/21R^3 = 704/(21 xx 125)`
`=> R^3 = 704/(21 xx 125) xx 21/88 = 8/125`
`=> R = 2/5 = 0.4 cm = 4 mm`
RELATED QUESTIONS
Find the surface area of a sphere of radius 14 cm.
`["Assume "pi=22/7]`
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.
Find the surface area of a sphere of radius 14 cm.
Find the total surface area of a hemisphere and a solid hemisphere each of radius 10 cm.
(Use ЁЭЬЛ = 3.14)
A largest sphere is to be carved out of a right circular cylinder of radius 7 cm and height 14 cm. Find the volume of the sphere.
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 largest sphere is cut off from a cube of side 6 cm. The volume of the sphere will be
Find the surface area of a sphere, if its volume is 38808 cubic cm. `(π = 22/7)`
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]
How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter?
