Question

A hollow metallic cylinder tube has an internal radius of 3cm and the height 21cm. The thickness f the matal is 0.5cm .The tube is melted and casted to form right circular cone of height 7cm find the radius of the cone.

Answer 1

22/7×3.5×21=66×3.5=231is volume of cylinder. 1/3×22/7 r×7=231
1/3×22×r=231
22r=77
r=7/2=3.5

Answer 2

Let the internal radius of the cylinder be r = 3 cm.

height of the cylinder be h = 21 cm

Thickness of the metal ( t )= 0.5 cm

∴ the external radius of the cylinder R = 3 + 0.5 = 3.5 cm

the volume of the metal = πR2h – πr2h = π(R2 – r2)h

= π(3.52 – 32)21

= π(12.25 – 9)21

= πx 3.25x 21 cm3

let the height of the cone be H = 7 cm

let the radius of the cone be R cm.

volume of the cone =(1/3) πR2H = (1/3)πR2 x 7 cm2

volume of the cone = volume of the melted metal

(1/3)πR2 x 7 cm2 = πx 3.25x 21 cm3

R2 = (3.25x21x3) / 7 = 3.25 x 9 = 29.25

∴R = 5.408 cm