Advertisements
Advertisements
Question
A hollow sphere of internal and external radii 2 cm and 4 cm respectively is melted into a cone of base radius 4 cm. Find the height and slant height of the cone.
Solution
Given that
Hollow sphere external radii = 4cm = `r_2`
Internal radii `(r_1)`=2cm
Cone base radius (R) = 4cm
Height = ?
Volume of cone = Volume of sphere
⇒ `1/3πr^2H=4/3π(R_2^3-R_1^3)`
⇒ `4^2H=4(4^3-2^3)`
⇒` H=H=(4xx56)/16=14cm`
Slant height =`sqrt(R^2+H^2)=sqrt(4^2+14^2)`
⇒ `l= sqrt(16+196)=sqrt(212)`
=14.56cm.
APPEARS IN
RELATED QUESTIONS
Find the volume of a sphere whose radius is 7 cm.
`["Assume "pi=22/7]`
A hemispherical tank has inner radius of 2.8 m. Find its capacity in litres.
A sphere of radius 5 cm is immersed in water filled in a cylinder, the level of water rises `5/3`cm. Find the radius of the cylinder.
A sphere, a cylinder and a cone have the same diameter. The height of the cylinder and also the cone are equal to the diameter of the sphere. Find the ratio of their volumes.
A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.
If the ratio of radii of two spheres is 4 : 7, find the ratio of their volumes.
A hemispherical tank of radius 1.75 m is full of water. It is connected with a pipe which empties the tank at the rate of 7 litres per second. How much time will it take to empty the tank completely?
The radius of a sphere is 2r, then its volume will be ______.
If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be 6 : π.
Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16 cm × 8 cm × 8 cm. When 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. [Use π = 3.14]
