Answer
Verified
467.7k+ views
Hint: First we’ll find the volume of both the figures. We have given that the volume of the cylinder and the cube are equal and the height of the cylinder and the edge of the cube is also equal using this we’ll get two equations.
Using, volume of a cylinder=$\pi {(radius)^2}height$ and Volume of cube=${\left( {edge} \right)^3}$
Therefore, using these equations we’ll have the value of the radius of the cylinder.
Complete step-by-step answer:
Given data: Height of cylinder(h)= edge of the cube
The volume of cylinder=volume of the cube
Let the edge of the cube be ‘a’ and the base radius of the cylinder be ‘r’
We, know that volume of a cylinder$ = \pi {(radius)^2}height$
Volume of cube$ = {\left( {edge} \right)^3}$
Therefore, the volume of the given cylinder$ = \pi {r^2}h$
And the volume of the cube$ = {a^3}$
According to the given data, the height of the cylinder and edge of the cube is equal
i.e. $a = h.......(i)$
and volume of both the figures are equal
i.e. volume of cylinder=volume of the cube
$ \Rightarrow \pi {r^2}h = {a^3}$
Substituting the value of ‘a’ from eq(i) , we get,
$ \Rightarrow \pi {r^2}h = {h^3}$
Dividing both sides by $\pi h$
$ \Rightarrow {r^2} = \dfrac{{{h^2}}}{\pi }$
Taking square root on both the sides
$ \Rightarrow r = \dfrac{h}{{\sqrt \pi }}$
Therefore, option(A) is correct.
Note: We don’t necessarily need the values of height and edge to solve for radius of cylinder here, we can get radius in terms of edge or length.
In this above solution we’ve used some formula regarding the cylinder and the cube.
Let us see some other formula related to the cylinder and the cube.
1.Total surface area of a cube$ = 6{(side)^2}$
2.Total surface area of the cylinder$ = 2\pi (radius)[height + radius]$
3.Curved surface area of cube$ = 4{(side)^2}$
4.Curved surface area of the cylinder$ = 2\pi (radius)(height)$
Using, volume of a cylinder=$\pi {(radius)^2}height$ and Volume of cube=${\left( {edge} \right)^3}$
Therefore, using these equations we’ll have the value of the radius of the cylinder.
Complete step-by-step answer:
Given data: Height of cylinder(h)= edge of the cube
The volume of cylinder=volume of the cube
Let the edge of the cube be ‘a’ and the base radius of the cylinder be ‘r’
We, know that volume of a cylinder$ = \pi {(radius)^2}height$
Volume of cube$ = {\left( {edge} \right)^3}$
Therefore, the volume of the given cylinder$ = \pi {r^2}h$
And the volume of the cube$ = {a^3}$
According to the given data, the height of the cylinder and edge of the cube is equal
i.e. $a = h.......(i)$
and volume of both the figures are equal
i.e. volume of cylinder=volume of the cube
$ \Rightarrow \pi {r^2}h = {a^3}$
Substituting the value of ‘a’ from eq(i) , we get,
$ \Rightarrow \pi {r^2}h = {h^3}$
Dividing both sides by $\pi h$
$ \Rightarrow {r^2} = \dfrac{{{h^2}}}{\pi }$
Taking square root on both the sides
$ \Rightarrow r = \dfrac{h}{{\sqrt \pi }}$
Therefore, option(A) is correct.
Note: We don’t necessarily need the values of height and edge to solve for radius of cylinder here, we can get radius in terms of edge or length.
In this above solution we’ve used some formula regarding the cylinder and the cube.
Let us see some other formula related to the cylinder and the cube.
1.Total surface area of a cube$ = 6{(side)^2}$
2.Total surface area of the cylinder$ = 2\pi (radius)[height + radius]$
3.Curved surface area of cube$ = 4{(side)^2}$
4.Curved surface area of the cylinder$ = 2\pi (radius)(height)$
Recently Updated Pages
10 Examples of Evaporation in Daily Life with Explanations
10 Examples of Diffusion in Everyday Life
1 g of dry green algae absorb 47 times 10 3 moles of class 11 chemistry CBSE
If the coordinates of the points A B and C be 443 23 class 10 maths JEE_Main
If the mean of the set of numbers x1x2xn is bar x then class 10 maths JEE_Main
What is the meaning of celestial class 10 social science 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?
How do you graph the function fx 4x class 9 maths CBSE
Who was the leader of the Bolshevik Party A Leon Trotsky class 9 social science CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Which is the largest saltwater lake in India A Chilika class 8 social science CBSE
Ghatikas during the period of Satavahanas were aHospitals class 6 social science CBSE