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ICSE Class 10 Mathematics Question 33 of 49

Multiple-Choice Questions — Question 33

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Question

Question 33

A right circular cone has the radius of the base equal to the height of the cone. If the volume of the cone is 9702 cu. cm, then the diameter of the base of the cone is :

  1. 21 cm

  2. 42 cm

  3. 21721\sqrt{7} cm

  4. 272\sqrt{7} cm

[Use π=227]\Big[\text{Use } \pi = \dfrac{22}{7}\Big]

Answer

Given,

Height of cone (h) = Radius of cone (r) = a cm (let)

A right circular cone has the radius of the base equal to the height of the cone. If the volume of the cone is 9702 cu. cm, then the diameter of the base of the cone is : Maths Competency Focused Practice Questions Class 10 Solutions.

Given,

Volume = 9702 cm3

∴13πr2h=9702⇒13×227×a2×a=9702⇒a3=9702×7×322⇒a3=441×21⇒a3=9261⇒a=92613=21 cm.\therefore \dfrac{1}{3}πr^2h = 9702 \\[1em] \Rightarrow \dfrac{1}{3} \times \dfrac{22}{7} \times a^2 \times a = 9702 \\[1em] \Rightarrow a^3 = \dfrac{9702 \times 7 \times 3}{22} \\[1em] \Rightarrow a^3 = 441 \times 21 \\[1em] \Rightarrow a^3 = 9261 \\[1em] \Rightarrow a = \sqrt[3]{9261} = 21 \text{ cm}.

Diameter = 2 × radius = 2 × 21 = 42 cm.

Hence, Option 2 is the correct option.