Question

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

Answer 1

the volume of hollow cylinder is equal to the volume of solid cylinder.

Answer 2

Answer:

The radius of the solid cylinder is 2.4 cm .

Step-by-step explanation:

Formula

$Volume\ of\ a\ cylinder = \pi r^{2} h$

Where r is the radius and h is the height of the cylinder .

As given

A hollow cylinder of height 3cm, is recast into solid cylinder of height 9cm. if external and internal radii of hollow cylinder are 4.3 cm and 1.1 cm respectively .

Let us assume that the external radius of the hollow cylinder is represented by u .

Let us assume that the interal radius of the hollow cylinder is represented by u .

Thus

$Volume\ of\ hollows\ cylinder\ material = \pi u^{2}h - \pi v^{2}h$

$\pi = 3.14$

Putting all the values in the above

Volume of hollow cylinder material = 3.14 × 3 × 4.3 × 4.3 - 3.14 × 3 × 1.1 × 1.1

                                                          = 174.18 - 11.4

                                                          = 162.78 cm ³

$Volume\ of\ solid\ cylinder= \pi r^{2}h$

                                                  = 3.14 × 9 × r²

                                                   = 28.26r²

Thus

Volume of the  hollow cylinder material = Volume of the solid cylinder

162.78 = 28.26r²

$r^{2}=\frac{162.78}{28.26}$

$r^{2}=5.76$

r = √ 5.76

r = 2.4 cm

Therefore the radius of the solid cylinder is 2.4 cm .