Answer
Verified
482.1k+ views
Hint: - Volume of spherical ball\[{\text{ = }}\dfrac{4}{3}\pi r_1^3\], (where ${r_1}$is the radius of the ball), and the volume of cylinder\[{{\text{V}}_C} = \pi {r^2}h\], (where r is the radius and h is the height of the cylinder)
Given data:
Radius of cylindrical tube \[\left( r \right) = 12cm\]
Depth of water in cylindrical tube\[\left( h \right) = 20cm\]
Volume of cylinder without rise\[{{\text{V}}_C} = \pi {r^2}h = \pi {\left( {12} \right)^2}\left( {20} \right) = 2880\pi c{m^3}\]
After dropping the spherical ball the level of water is raised by 6.75 cm.
$ \Rightarrow $New depth of water in cylindrical tube\[\left( {{h_1}} \right) = 20 + 6.75 = 26.75cm\]
$ \Rightarrow $New cylindrical volume \[{\text{ = }}\pi {r^2}{h_1} = \pi {\left( {12} \right)^2}\left( {26.75} \right) = 3852\pi c{m^3}\]
Volume of spherical ball\[{\text{ = }}\dfrac{4}{3}\pi r_1^3\], (where ${r_1}$is the radius of the ball)
Therefore new cylindrical volume $ = $ Volume of spherical ball$ + $ Volume of cylinder \[{{\text{V}}_C}\]without rise
\[
\Rightarrow 3852\pi = \dfrac{4}{3}\pi r_1^3 + 2880\pi \\
\Rightarrow \dfrac{4}{3}\pi r_i^3 = 972\pi \\
\Rightarrow r_1^3 = 729 = {\left( 9 \right)^3} \\
\Rightarrow {r_1} = 9cm \\
\]
So, the radius of the ball is 9cm.
Note: - In such types of questions always remember the formula of volume of cylinder and spherical ball which is stated above, then using these formulas, calculate the new volume of the cylindrical tub, when spherical ball is dropped in cylindrical tub and simplify, we will get the required radius of the ball.
Given data:
Radius of cylindrical tube \[\left( r \right) = 12cm\]
Depth of water in cylindrical tube\[\left( h \right) = 20cm\]
Volume of cylinder without rise\[{{\text{V}}_C} = \pi {r^2}h = \pi {\left( {12} \right)^2}\left( {20} \right) = 2880\pi c{m^3}\]
After dropping the spherical ball the level of water is raised by 6.75 cm.
$ \Rightarrow $New depth of water in cylindrical tube\[\left( {{h_1}} \right) = 20 + 6.75 = 26.75cm\]
$ \Rightarrow $New cylindrical volume \[{\text{ = }}\pi {r^2}{h_1} = \pi {\left( {12} \right)^2}\left( {26.75} \right) = 3852\pi c{m^3}\]
Volume of spherical ball\[{\text{ = }}\dfrac{4}{3}\pi r_1^3\], (where ${r_1}$is the radius of the ball)
Therefore new cylindrical volume $ = $ Volume of spherical ball$ + $ Volume of cylinder \[{{\text{V}}_C}\]without rise
\[
\Rightarrow 3852\pi = \dfrac{4}{3}\pi r_1^3 + 2880\pi \\
\Rightarrow \dfrac{4}{3}\pi r_i^3 = 972\pi \\
\Rightarrow r_1^3 = 729 = {\left( 9 \right)^3} \\
\Rightarrow {r_1} = 9cm \\
\]
So, the radius of the ball is 9cm.
Note: - In such types of questions always remember the formula of volume of cylinder and spherical ball which is stated above, then using these formulas, calculate the new volume of the cylindrical tub, when spherical ball is dropped in cylindrical tub and simplify, we will get the required radius of the ball.
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