Answer
Verified
480.9k+ views
Hint: We are going to solve the given problem by using the formula of finding the volume of a spherical object.
It is known that the volume of a sphere with radius $r$ is given by $\frac{4}{3}\pi {r^3}$
Let the radius of the original ball be $R$.
So the volume of the original spherical ball with $$R = 3$$ is equal to $$\frac{4}{3}\pi {(3)^3}$$
Now the original ball is melted to form three balls of different sizes.
Let the radii of three resulting spherical balls be ${r_1},{r_2},{r_3}$ respectively.
Given ${r_1} = 1.5cm$ & ${r_2} = 2cm$.
$ \Rightarrow {V_{total}} = {V_1} + {V_2} + {V_3}$
$ \Rightarrow \frac{4}{3}\pi {R^3} = \frac{4}{3}\pi ({r_1}^3 + {r_2}^3 + {r_3}^3)$
$ \Rightarrow {r_3}^3 = {3^3} - {1.5^3} - {2^3} = 15.625$
Hence ${r_3} = 2.5cm$
$\therefore $The radius of the third ball = 2.5cm
Note: In the given problem it is said that the spherical ball of radius 3cm is melted to form three spherical balls. So the volume of the original spherical ball is equal to the sum of the volumes of the three balls.
It is known that the volume of a sphere with radius $r$ is given by $\frac{4}{3}\pi {r^3}$
Let the radius of the original ball be $R$.
So the volume of the original spherical ball with $$R = 3$$ is equal to $$\frac{4}{3}\pi {(3)^3}$$
Now the original ball is melted to form three balls of different sizes.
Let the radii of three resulting spherical balls be ${r_1},{r_2},{r_3}$ respectively.
Given ${r_1} = 1.5cm$ & ${r_2} = 2cm$.
$ \Rightarrow {V_{total}} = {V_1} + {V_2} + {V_3}$
$ \Rightarrow \frac{4}{3}\pi {R^3} = \frac{4}{3}\pi ({r_1}^3 + {r_2}^3 + {r_3}^3)$
$ \Rightarrow {r_3}^3 = {3^3} - {1.5^3} - {2^3} = 15.625$
Hence ${r_3} = 2.5cm$
$\therefore $The radius of the third ball = 2.5cm
Note: In the given problem it is said that the spherical ball of radius 3cm is melted to form three spherical balls. So the volume of the original spherical ball is equal to the sum of the volumes of the three balls.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Change the following sentences into negative and interrogative class 10 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE