Question

A hollow garden roller 56 cm wide with base area 154 cm sq is made of 4 cm thick iron . Find volume of iron

Answer 1

Solution :-

Width of the roller = Height of the roller = 56 cm

Base area = 154 sq cm

Thickness of the iron sheet = 4 cm

Let inner radius be 'r' cm and the outer radius will be 'R' = (r + 4) cm

Volume of iron = Volume of roller with outer radius (R) - Volume of roller with inner radius(r)

Volume of iron = (πR²h) - (πr²h)

= 22/7*h(R² - r²)

Base area = 22/7*R²

⇒ 154 = 22/7*R²

⇒ R² = (154*7)/22

⇒ R² = 1078/22

⇒ R² = 49

⇒ R = √49

⇒ R = 7 cm

So, outer radius is 7 cm

Since, R = r + 4

⇒ 7 = r + 4

⇒ r = 7 - 4

⇒ r = 3 cm

So, inner radius is 3 cm

Volume of iron = 22/7*56*(7² - 3²)

⇒ 22/7*56*(49 - 9)

⇒ 22/7*56*40

⇒ 49280/7

= 7040 cu cm

So, volume of iron is 7040 cu cm

Answer.