Question

The volume of 1 cm thick 21 cm long pipe is 1650 cmº. Find its inner and outer radii.​

Answer 1

GIVEN :-

• Volume of 1cm thick 21cm long pipe is 1650cm³.

TO FIND :-

• Inner radii(r) and Outer radii(R).

TO KNOW :-

★ Volume of Cylinder = πr²h

SOLUTION :-

Let the inner radii be 'r' .

Outer radii is 1cm greater than inner radii .

Outer radii is 'r+1'.

Volume of pipe = Volume with Outer radius - Volume with inner radius

→ Volume of pipe = πR²h - πr²h

→ 1650 = πh(R² - r²)

→ 1650 = (22/7) × 21 × [ (r+1)² + r² ]

→ 1650 = 22 × 3 [ r² + 2r + 1 + r² ]

→ 1650 = 66 [ 2r² + 2r + 1 ]

→ 1650/66 = 2r² + 2r + 1

→ 25 = 2r² + 2r + 1

→ 2r² + 2r - 24 = 0

Solving by splitting middle term ,

→ 2r² + 8r - 6r - 24 = 0

→ 2r(r + 4) - 6(r + 4) = 0

→ (2r - 6)(r + 4) = 0

→ 2r - 6 = 0 or r + 4 = 0

→ r = 3cm or r = -4cm

Length is scalar quantity and hence , can't be negative.

So, r = 3cm

• Inner radii = r = 3cm
• Outer radii = r + 1 = 4cm

Therefore , Inner radii is 3cm and outer radii is 4cm.