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A cylindrical well of radius 7 cm and height 10 cm is dug and the mud is spread out evenly around the well having the width of 3.5 cm. What is the height of mud spread around the well? (Take π = 22/7)

A cylindrical well of radius 7 cm and height 10 cm is dug and the mud is spread out evenly around the well having the width of 3.5 cm. What is the height of mud spread around the well? (Take π = 22/7) Correct Answer 8 cm

Given:

Radius of cylindrical well = 7 cm

Height of cylindrical well = 10 cm

Width of mud = 3.5 cm

Concepts used:

Volume of cylinder well = πr2h

Volume of mud spread around well = π × (R2 – r2) × h

Calculation:

Volume of cylindrical well = πr2h

⇒ 22/7 × (7)2 × 10 cm = 1,540 cm3

Inner radius (r) of mud = 7 cm

Outer radius of mud = Inner radius of mud + width = (7 + 3.5) cm = 10.5 cm

Volume of mud spread around well = π × (R2 – r2) × h

⇒ 22/7 × × 10 cm3

⇒ 22/7 × (10.5 – 7) × (10 + 7.5) × h cm3

⇒ 192.5 × h cm3

Volume of cylindrical well = Volume of mud spread around well

⇒ 1,540 cm3 = 192.5 × h cm3

⇒ h = 1,540/192.5 cm

⇒ h = 8 cm

∴ Height of mud spread around wall is equal to 8 cm.

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