Advertisements
Advertisements
प्रश्न
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.
उत्तर
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
संबंधित प्रश्न
The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?
A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm (see the given figure). The thickness of the plank is 5 cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per cm2 and the rate of painting is 10 paise per cm2, find the total expenses required for polishing and painting the surface of the bookshelf.
The front compound wall of a house is decorated by wooden spheres of diameter 21 cm, placed on small supports as shown in the given figure. Eight such spheres are used for this purpose, and are to be painted silver. Each support is a cylinder of radius 1.5 cm and height 7 cm and is to be painted black. Find the cost of paint required if silver paint costs 25 paise per cm2 and black paint costs 5 paise per cm2.
A cylinder whose height is two thirds of its diameter, has the same volume as a sphere of radius 4 cm. Calculate the radius of the base of the cylinder.
A cylindrical tub of radius 16 cm contains water to a depth of 30 cm. A spherical iron ball is dropped into the tub and thus level of water is raised by 9 cm. What is the radius of the ball?
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.
If the ratio of radii of two spheres is 4 : 7, find the ratio of their volumes.
A solid sphere and a solid hemisphere have an equal total surface area. Prove that the ratio of their volume is `3sqrt(3):4`
Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r units.
The radius of a sphere is 2r, then its volume will be ______.
