The volume of the metal of a cylindrical pipe is 748 cm3. The length o

1.	The volume of the metal of a cylindrical pipe is 748 cm3. The length of the pipe is 14 cm and its external radius is 9 cm. What is its thickness ? (Take π = 22/7) (a) 1 cm (b) 5.2 cm (c) 2.3 cm (d) 3.7 cm
Answer» (a) 1 cm. Let the thickness of the pipe be a cm. External Radius = 9 cm. ∴ Internal radius = (9 – a) cm. Given, Volume of metal = 748 cm³ ⇒ (π × 92 × 14) – (π × (9 – a)² × 14) = 748 ⇒ π × 14 × [81 – (81 + a² – 18a)] = 748 ⇒ –a² + 18a = \(\frac{748}{π\times14}=\frac{748\times7}{22\times14}=17\) ⇒ a² – 18a + 17 = 0 ⇒ (a – 17) (a – 1) = 0 ⇒ a = 1 or 17, but a = 17 is inadmissible.

The volume of the metal of a cylindrical pipe is 748 cm3. The length of the pipe is 14 cm and its external radius is 9 cm. What is its thickness ? (Take π = 22/7) (a) 1 cm (b) 5.2 cm (c) 2.3 cm (d) 3.7 cm

Answer»

(a) 1 cm.

Let the thickness of the pipe be a cm.

External Radius = 9 cm.

∴ Internal radius = (9 – a) cm.

Given, Volume of metal = 748 cm³

⇒ (π × 92 × 14) – (π × (9 – a)² × 14) = 748

⇒ π × 14 × [81 – (81 + a² – 18a)] = 748

⇒ –a² + 18a = \(\frac{748}{π\times14}=\frac{748\times7}{22\times14}=17\)

⇒ a² – 18a + 17 = 0

⇒ (a – 17) (a – 1) = 0

⇒ a = 1 or 17, but a = 17 is inadmissible.