Question

detailed explanation please

Both the questions

Answer 1

8. Let thickness of the hollow cylinder be x cm.

External radius of the hollow cylinder, R = 8 cm

∴ Internal radius of the hollow cylinder, r = (8 – x) cm

Height of the cylinder, h = 10 cm
 

It is given that the total surface area of the hollow cylinder is 338Π cm2.

∴ 2ΠRh + 2Πrh + 2Π (R2 – r2) = 338 Π

⇒ 2Π (R + r) h + (R – r) (R + r) = 338Π

⇒ (R + r) (R – r + h) = 169

⇒ {8 + (8 – x)} {8 – (8 – x) + 10} = 169

⇒ {16 – x) (10 + x) = 169

⇒ 160 + 6x – x2 = 169

⇒ x2 – 6x + 9 = 0

⇒ (x – 3)2 = 0

⇒ x = 3

Thus, the thickness of the cylinder is 3 cm.


9. Given  radius of the cylindrical vessel 70 cm

  height of the cylindrical vessel 140cm

  rate of tin plating Rs3.50 per 1000 square centimetre

Requirement: Cost of tin-plating it on both the inner and outer surface

Total surface area of a vessel = area of inner and outer side of the base + area of inner and outer curved surface

=> 2(πr2 + 2πrh)

=>2πr(r+ 2h)

=> 2*22*70/7(70 +2*140)  [since r = 70cm,h = 140cm]

=> 154000cm2

=>cost of painting at the rate of Rs3.50 per 1000 square centimetre = 154000 * 3.50/1000

=> Rs 539

Therefore cost of painting the cylindrical vessel is Rs539.