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ICSE Class 10 Mathematics Question 14 of 49

Multiple-Choice Questions — Question 14

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Question 14

The ratio of diameter to height of a Borosil cylindrical glass is 3 : 5. If the actual diameter of the glass is 6 cm, then the curved surface area of the glass is :

  1. 120π

  2. 60π

  3. 30π

  4. 18π

Answer

Given,

Ratio of diameter to height of a Borosil cylindrical glass is 3 : 5.

⇒dh=35⇒6h=35⇒h=6×53⇒h=10 cm.\Rightarrow \dfrac{d}{h} = \dfrac{3}{5} \\[1em] \Rightarrow \dfrac{6}{h} = \dfrac{3}{5} \\[1em] \Rightarrow h = \dfrac{6 \times 5}{3} \\[1em] \Rightarrow h = 10 \text{ cm}.

Radius = Diameter2=62\dfrac{\text{Diameter}}{2} = \dfrac{6}{2} = 3 cm.

By formula,

Curved surface area of glass = 2πrh

= 2π × 3 × 10

= 60π cm2.

Hence, Option 2 is the correct option.