A hollow cylindrical tube 20 cm long is made of iron and its external

1.	A hollow cylindrical tube 20 cm long is made of iron and its external diameter is 8 cm. The volume of iron used in making the tube is 440 cm3. What is the thickness of the tube? (a) 1 cm (b) 0.5 cm (c) 2 cm (d) 1.5 cm
Answer» (a) 1 cm Let the internal radius of the tube be r cm. External radius = \(\frac82\) cm = 4 cm, Height = 20 cm ∴ Volume of iron used in the tube = π(4² - r²) x 20 cm Given, π x (16 - r²) x 20 = 440 ⇒ \(\frac{22}{7}\times20\times(16-r^2) = 440\) ⇒ 16 – r² = 7 ⇒ r² = 16 – 7 = 9 ⇒ r = 3 ∴ Thickness of tube = 4 cm – 3 cm = 1 cm.

A hollow cylindrical tube 20 cm long is made of iron and its external diameter is 8 cm. The volume of iron used in making the tube is 440 cm3. What is the thickness of the tube? (a) 1 cm (b) 0.5 cm (c) 2 cm (d) 1.5 cm

Answer»

(a) 1 cm

Let the internal radius of the tube be r cm.

External radius = \(\frac82\) cm = 4 cm,

Height = 20 cm

∴ Volume of iron used in the tube = π(4² - r²) x 20 cm

Given, π x (16 - r²) x 20 = 440

⇒ \(\frac{22}{7}\times20\times(16-r^2) = 440\)

⇒ 16 – r² = 7 ⇒ r² = 16 – 7 = 9 ⇒ r = 3

∴ Thickness of tube = 4 cm – 3 cm = 1 cm.