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RD Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1 Solutions

Question - 11 : - Twenty cylindrical pillars of the Parliament House are to be cleaned. If the diameter of each pillar is 0.50 m and height is 4 m. What will be the cost of cleaning them at the rate of ₹2.50 per square metre? [NCERT]

Answer - 11 : -

Number of pillars = 20
Diameter of one pillar = 0.50 m

Question - 12 : - A solid cylinder has total surface area of 462 cm2.Its curved surface area is one- third of its total surface area. Find theradius and height of the cylinder.

Answer - 12 : - Total surface of solid cylinder = 462 cm2
Curved surface area = 1/3 of total surface area

Question - 13 : - The total surface area of a hollow metal cylinder, open at both ends of external radius 8 cm and height 10 cm is 338 π cm2. Taking r to be inner radius, obtain an equation in r and use it to obtain the thickness of the metal in the cylinder.

Answer - 13 : -

Total surface area of a hollow metal cylinder = 338π cm2
Let R be the outer radius, r be inner radius and h be the height of thecylinder of the cylinder
∴ 2πRh +2πrh + 2πR2 – 2πr2 = 338π
R = 8 cm, h = 10 cm
⇒ 2πh (R+ r) + 2π(R2 – r2) = 338π
⇒Dividing by 2π , we get
⇒ h(R +r) + (R2 – r2) = 169
⇒ 10(8 +r) + (8 + r) (8 – r) = 169
⇒ 80 +10r + 64 – r2 = 169
⇒ 10r –r2 + 144 – 169 = 0
⇒ r2 –10r + 25 = 0
⇒ (r-5)2 =0
⇒ r = 5
∴Thickness of the metal = R – r = 8 – 5 = 3 cm

Question - 14 : - Find the lateral curved surface area of a cylinderical petrol storage tank that is 4.2m in diameter and 4.5 m high. How much steel was actually used, if 1/12 of steel actually used was wasted in making the closed tank? [NCERT]

Answer - 14 : - Diameter of a cylinderical tank = 4.2 m

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