Advertisements
Advertisements
प्रश्न
Eight metallic spheres; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere.
Advertisements
उत्तर
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`
APPEARS IN
संबंधित प्रश्न
A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of ₹ 16 per 100 cm2.
`["Assume "pi=22/7]`
A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and recast into small cones of base radius 2 cm and height 8 cm. Find the number of cones.
Find the surface area of a sphere of radius 14 cm.
Find the surface area of a sphere of diameter 21 cm.
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.
A hemi-spherical bowl has negligible thickness and the length of its circumference is 198 cm. Find the capacity of the bowl.
A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder. If the radius of the sphere is r, then the volume of the cylinder is
Find the surface area and volume of sphere of the following radius. (π = 3.14 )
3.5 cm
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?
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.
