A hollow garden roller 63 cm wide with a girth of 440 cm, is made of 4

1.	A hollow garden roller 63 cm wide with a girth of 440 cm, is made of 4 cm thick iron. Find the volume of the iron.
Answer» Given, Width of hollow cylinder = 63 cm Girth (perimeter) = 440 cm Let external radius of cylinder = R cm So, 2πr = 440 = R = \(\cfrac{440\times7}{2\times22}\) = 70 cm = inner radius = outer radius – thickness = 70 – 4 = 66 cm ∴ volume of iron = π( R² - r²)h = \(\cfrac{22}7\times\)(70² - 66²)\(\times\)63 = \(\cfrac{22}7\times\)136\(\times\)4\(\times\)63 = 107712 cm³

A hollow garden roller 63 cm wide with a girth of 440 cm, is made of 4 cm thick iron. Find the volume of the iron.

Answer»

Given,

Width of hollow cylinder = 63 cm

Girth (perimeter) = 440 cm

Let external radius of cylinder = R cm

So, 2πr = 440

= R = \(\cfrac{440\times7}{2\times22}\) = 70 cm

= inner radius = outer radius – thickness = 70 – 4 = 66 cm

∴ volume of iron = π( R² - r²)h = \(\cfrac{22}7\times\)(70² - 66²)\(\times\)63

= \(\cfrac{22}7\times\)136\(\times\)4\(\times\)63 = 107712 cm³