Question

a hollow metal cylinder has inner radius of 3cm and height 21cm the thickness of the metal is 0.5 cm. the tube is melted and cast into a right circular the height 7 cm.

Answer 1

Hey there!

Internal radius, r = 3 cm

Height of cylinder, h = 21 cm

Thickness of the Metal, t = 0.5 cm

∴ The External radius of the cylinder:
R = 3 + 0.5 = 3.5 cm

Now,
Volume of the metal = πR^h – πr^2h

= π(R^2 – r^2)h

= π(3.52 – 32)21

= π(12.25 – 9)21

= π x 3.25 x 21 Cubic cm.

Let the height of the cone be H = 7 cm
& the radius of the cone be R cm.

Volume of the cone = (1/3) × πR^2H

= (1/3)πR^2 x 7

Volume of the cone = Volume of the melted metal

(1/3)πR2 x 7 = π x 3.25 x 21

$R^2$ = (3.25x21x3) / 7 = 3.25 x 9 = 29.25

∴R = 5.408 cm

Hence,
radius of Cone = 5.408 cm

Cheers!