Advertisements
Advertisements
Question
The diameters of the internal and external surfaces of a hollow spherical shell are 6 cm and 10 cm respectively. If it is melted and recast and recast into a solid cylinder of diameter 14 cm, find the height of the cylinder.
Solution
Internal diameter of hollow spherical shell = 6cm
Internal radius of hollow spherical shell =`6/3=3` cm
External diameter of hollow spherical shell = 10 cm
External radius of hollow spherical shell = `10/2=5`cm
Diameter of cylinder = 14 cm
Radius of cylinder`=14/2=7`cm
Let height of cylinder = xcm
According to the question
Volume of cylinder = Volume of spherical shell
⇒ `pi(7)^2x xx=4/3pi(5^3-3^3)`
⇒`49x xx=4/3(125-27)`
⇒`49x xx=4/3xx98`
`x=(4xx98)/(3xx49)=8/3cm`
∴Height off cylinder=`8/3cm`
APPEARS IN
RELATED QUESTIONS
A hollow sphere of internal and external radii 2cm and 4cm is melted into a cone of basse radius 4cm. find the height and slant height of the cone______?
An iron spherical ball has been melted and recast into smaller balls of equal size. If the radius of each of the smaller balls is 1/4 of the radius of the original ball, how many such balls are made? Compare the surface area, of all the smaller balls combined together with that of the original ball.
12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. The diameter of each sphere is
The ratio between the radius of the base and the height of a cylinder is 2 : 3. If the volume of the cylinder is 12936 cm3, then find the radius of the base of the cylinder.
Three cubes of a metal whose edges are in the ratio 3 : 4 : 5 are melted and converted into a single cube whose diagonal is `12sqrt(3)` cm. Find the edges of the three cubes.
Match the following columns:
| Column I | Column II |
| (a) A solid metallic sphere of radius 8 cm is melted and the material is used to make solid right cones with height 4 cm and base radius of 8 cm. How many cones are formed? | (p) 18 |
| (b) A 20-m-deep well with diameter 14 m is dug up and the earth from digging is evenly spread out to form a platform 44 m by 14 m. The height of the platform is ...........m. |
(q) 8 |
| (c) A sphere of radius 6 cm is melted and recast in the shape of a cylinder of radius 4 cm. Then, the height of the cylinder is ......... cm. |
(r) 16 : 9 |
| (d) The volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is ....... . |
(s) 5 |
The radius of a solid right circular cylinder increases by 20% and its height decreases by 20%. Find the percentage change in its volume.
If the radius of base of a right circular cylinder is halved, keeping the height same, the ratio of the volume of the reduced cylinder to that of the original cylinder is ______.
The rain water from a roof of dimensions 22 m × 20 m drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m. If the rain water collected from the roof just fill the cylindrical vessel, then find the rainfall in cm.
The sum of the length, breadth and height of a cuboid is `6sqrt(3)` cm and the length of its diagonal is `2sqrt(3)` cm. The total surface area of the cuboid is ______.
