Advertisements
Advertisements
प्रश्न
A spherical ball of radius 3cm is melted and recast into three spherical balls. The radii of the two of balls are 1.5cm and 2cm . Determine the diameter of the third ball?
उत्तर
Given that a spherical ball of radius 3cm
We know that Volume of a sphere`=4/3pir^2`
So its volume(v)`=4/3pi(3)^2`
Given that ball is melted and recast into three spherical balls
Radii of first ball (v1)=`4/3pi(1.5)^3`
Radii of second ball(v2)=`4/3pi(2)^3`
Radii of third ball ___________?
Volume of third ball `=4/3pir^3=v_3`
Volume of spherical ball is equal to volume of 3 small spherical balls
⇒ `4/3pir^2+4/3pi(1.5)^3+4/3pi(2)^3=4/3pi(3)^3`
⇒ `r^2+(1.5)^3+(2)^3=(3)^3`
⇒ `r^3=3^3-1.5^3-2^3`
⇒ `r-(15.6)1/3`
⇒ `r=2.5cm`
Diameter (d) = 2r = 2 x 2.5 = 5cm
∴Diameter of third ball = 5cm.
संबंधित प्रश्न
Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. if each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.) [use `pi = 22/7`]
A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm3 of iron has approximately 8 g mass. [Use π = 3.14]
500 persons have to dip in a rectangular tank which is 80m long and 50m broad. What is the rise in the level of water in the tank, if the average displacement of water by a person is 0.04m3 .
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.
The difference between outside and inside surface areas of cylindrical metallic pipe 14 cm long is 44 m2. If the pipe is made of 99 cm3 of metal, find the outer and inner radii of the pipe.
A right circular cylinder having diameter 12 cm and height 15 cm is full ice-cream. The ice-cream is to be filled in cones of height 12 cm and diameter 6 cm having a hemispherical shape on the top. Find the number of such cones which can be filled with ice-cream.
A solid toy is in the form of a hemisphere surmounted by a right circular cone. height of the cone is 2 cm and the diameter of the base is 4 cm. If a right circular cylinder circumscribes the toy, find how much more space it will cover.
A hemispherical tank, full of water, is emptied by a pipe at the rate of `25/7`litres per sec.
How much time will it take to empty half the tank if the diameter of the base of the tank is 3 m?
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 adjoining figure represents a solid consisting of a cylinder surmounted by a cone at one end and a hemisphere at the other. Find the volume of the solid.
