Question

the metallic right circular cylinder is 15 cm high and the diameter of the base is 14 cm It is melted and recast into another cylinder with radius 4 centimetre find the height and the curved surface area of the new cylinder

Answer 1

h=15 cm                 R=4 cm

d=14 cm

r=7 cm

volume of cylinder 1 = volume of cylinder 2

22/7 * 7 * 7 * 15          = 22/7 * 4 * 4 * H

7 x 7 x 15 /4 x 4          = H

735 / 16                       = H

C.S.A. of cylinder =2 x 22/7 x 4 x 735/16

                             = 1155 square cm

Answer 2

Answer:

height of the new cylinder = 45.93 cm

curved surface area of new cylinder = 1153.76 $cm^{2}$

Step-by-step explanation:

Given right circular cylinder height h = 15 cm

and diameter of the base  2r = 14

radius of the right circular cylinder r = 7 cm

the volume of the circular cylinder  v = $\pi r^{2} h$

                                                            v = $\frac{22}{7}$ ×7×7× 15

                                                            v = 2310 $cm^{3}$

given that the cylinder is melted and recast into another cylinder

radius of the new cylinder v = 2310 $cm ^{3}$

the radius of the  new cylinder  r = 4 cm

we need to find height and curved surface area of the new cylinder

here the volume of the cylinder remains as same

 volume of the new cylinder = $\pi r^{2} h$ = 2310

                                         ⇒  $\frac{22}{7}$ ×4 ×4 ×h = 2310

                                         ⇒ h = $\frac{2310 (7) }{22(4)(4)}$

                                         ⇒ h = $\frac{16170}{352}$ =  45.93

the height of the new cylinder h = 45.93 cm

curved surface area of the new cylinder  = 2 $\pi rh$

                                         ⇒  $\frac{22}{7}$ ×2 ×4 ×45.93

                                         ⇒ $\frac{22}{7}$ × 367.44

                                         ⇒ 1153.76  $cm^{2}$  approximately