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Doctors Medicines MCQs Q&A

  1. 690π
  2. 500π
  3. 450π
  4. 590π
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1 Answers

Option 4 : 590π

Given:

A cylindrical Toy, whose base diameter is 10 cm. The cost to cover its curved surface area at the rate of Rs. 0.2 sqcm is Rs. 330. Now a cone having same base diameter as cylinder is mounted on cylinder. If total height of the Toy is 64.5 cm. 

Formula Used :

Curved surface are of cylinder = 2πrh

l = slant height = √h2 + r2

Calculations:

Let the height of the cylinder is h cm, curved surface area is A cm

∵ Total cost to cover the curved surface area at Rs.0.2 sqcm is 330

∴ A × 0.2 = 330

⇒ A = 1650 sqcm

⇒ A = 2π × 5× h = 1650, (∵ curved surface are of cylinder = 2πrh)

⇒ h = 52.5 cm

∵ Total height of the toy (cone + cylinder) = 64.5 cm

∴ Height of the cone = 64.5 – 52.5 = 12 cm

⇒ Total curved surface area (cylinder + cone) = 2πrh + πrl (∵ l = slant height = √122 + 52 = 13 cm)

⇒ πr(2h + l) = π × 5 (2 × 52.5 + 13) = π × 5 × 118 = 590π 

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