Q2,Q3,Q4,Q5

​Q2). If the perimeter of a square is (4y + 12) m, then find the length of its diagonal.

Q3) A right circular cylinder, a right circular cone and a hemisphere are all having equal base area and height. Find the ratio of their volumes.


Q4). There is a cylinder circumscribing the hemisphere such that their bases are common. Find the ratio of their volumes.

Q5). A cone and a cylinder have the same base area. They also have the same curved surface area. If the height of the cylinder is 3m, then find slant height of the cone.

Dear Student,

Please find below the solution to the asked query:

2 ) Given :  Perimeter of square = ( 4 y  + 12 ) m

We know perimeter of square = 4 ( Side ) , So

4 ( Side ) = ( 4 y  + 12 ) ,

4 ( Side ) = 4 ( y  + 3 ) ,

Side = ( y  + 3 ) m

We know diagonal of square = $\sqrt{2}$ ( Side ) , So

Length of diagonal of given square = $\sqrt{2}$( y  + 3 ) m                                        ( Ans )


3 ) Given :  A right circular cylinder, a right circular cone and a hemisphere are all having equal base area and height.

Let , Height of  a right circular cylinder, a right circular cone and a hemisphere = h 

And

Radius of  a right circular cylinder, a right circular cone and a hemisphere = r 


And we know height of hemisphere = Radius of hemisphere , So,

h = r                                                             --- ( 1 )

We know :  Volume of  a right circular cylinder = $\mathrm{\pi }$r² h  , Substitute value from equation 1 we get :

Volume of  given right circular cylinder = $\mathrm{\pi }$r²( r ) = $\mathrm{\pi }$r³  

And

Volume of  a right circular cone = $\frac{1}{3}$$\mathrm{\pi }$r² h  , Substitute value from equation 1 we get :

Volume of  given right circular cylinder = $\frac{1}{3}$$\mathrm{\pi }$r²( r ) = $\frac{1}{3}$$\mathrm{\pi }$r³  

And

Volume of  a hemisphere = $\frac{2}{3}$$\mathrm{\pi }$r³  

Then,

Volume of a right circular cylinder : Volume of  a right circular cone : Volume of hemisphere = $\mathrm{\pi }$r³  : $\frac{1}{3}$$\mathrm{\pi }$r³   : $\frac{2}{3}$$\mathrm{\pi }$r³ , 

Volume of a right circular cylinder : Volume of  a right circular cone : Volume of hemisphere = 1 : $\frac{1}{3}$  : $\frac{2}{3}$

Volume of a right circular cylinder : Volume of  a right circular cone : Volume of hemisphere = 3 : 1  : 2                      ( Ans )


Hope this information will clear your doubts about topic.

For remaining queries we request you to post them in separate threads to have rapid assistance from our experts.

Regards