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.
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
Find the surface area of a sphere of diameter 14 cm.
`["Assume "pi=22/7]`
A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones.
Two solid spheres of radii 2 cm and 4 cm are melted and recast into a cone of height 8 cm. Find the radius of the cone so formed.
Find the surface area of a sphere of radius 5.6 cm .
Find the surface area of a sphere of radius 14 cm.
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?
How many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 cm?
A hollow sphere of internal and external diameter 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.
Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r cm.
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?
Mark the correct alternative in each of the following:
In a sphere the number of faces is
The model of a building is constructed with the scale factor 1 : 30.
(i) If the height of the model is 80 cm, find the actual height of the building in meters.
(ii) If the actual volume of a tank at the top of the building is 27m3, find the volume of the tank on the top of the model.
Find the volume of a sphere, if its surface area is 154 sq.cm.
A solid metallic cylinder has a radius of 2 cm and is 45 cm tall. Find the number of metallic spheres of diameter 6 cm that can be made by recasting this cylinder .
The surface area of a solid metallic sphere is 2464 cm2. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate : the number of cones recast. `("Take" pi =22/7)`
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.
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 two spheres are in the ratio of 1 : 3. Find the ratio between their volume.
The cylinder of radius 12 cm have filled the 20 cm with water. One piece of iron drop in the stands of water goes up 6.75 cm. Find the radius of sphere piece.
The radius of a sphere increases by 25%. Find the percentage increase in its surface area
