Question

a hollow cylinder of height 3 cm is recast into a solid cylinder of height 9cm. if the external and internal radii of hollow cylinder are 4.3 cm and 1.1 cm then find the radius of the solid cylinder

Results in English

Answer 1

for both cylinder volume will be equal.

volume of hollow cylinder = pi x h x(R1^2-R2^2)
                                         = 3.14 x 3 x(4.3^2-1.1^2)
                                         = 9.42 x 17.28
                                         = 162.7 meter cube

volume of cyinder = pi x r^2 x h
                            
                             = 3.14 x 9 r^2 = 162.7
                            
                             = 28.26 x r^2  = 162.7
                           
                              = r^2 = 162.7/28.26

                              = r^2 = 5.75   

                                RADIUS = square root of 5.75 or 5.75^1/2
 

Answer 2

Answer:

The radius of the solid cylinder is 2.39 cm.

Step-by-step explanation:

Given : A hollow cylinder of height 3 cm is recast into a solid cylinder of height 9cm. if the external and internal radii of hollow cylinder are 4.3 cm and 1.1 cm.

To find : The radius of the solid cylinder?

Solution :

For both cylinder volume will be equal.

Volume of hollow cylinder,

$V=\pi \times h \times(R_1^2-R_2^2)$

$V=(3.14)\times 3\times(4.3^2-1.1^2)$

$V=9.42\times 17.28$

$V=162.7m^3$

Volume of cylinder,

$v=\pi \times r^2 \times h$

$v=(3.14)\times r^2\times 9$

$v=28.26r^2$

Both volume are equal,

$V=v$

$162.7=28.26r^2$

$r^2=\frac{162.7}{28.26}$

$r^2=5.75$                          

$r=\sqrt{5.75}$         

$r=2.39$      

The radius of the solid cylinder is 2.39 cm.