Question : The volume of a cone whose radius of a base and height are $r$ cm and $h$ cm respectively, is 400 cm3. What will be the volume of a cone whose radius of base and height are $2r$ cm and $h$ cm respectively?
Option 1: 100 cm3
Option 2: 1600 cm3
Option 3: 1200 cm3
Option 4: 800 cm3
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Correct Answer: 1600 cm 3
Solution : Given: The volume of a cone whose radius of a base and height are $r$ cm and $h$ cm respectively, is 400 cm 3 . The volume of a cone whose radius of base and height are $r$ cm and $h$ cm respectively $=\frac{1}{3}\pi r^2h$. According to the question, $\frac{1}{3}\times\frac{22}{7}\times r^2h=400$ ⇒ $ r^2h=\frac{400\times 7\times 3}{22}=\frac{4200}{11}$ The volume of a cone whose radius of base and height are $2r$ cm and $h$ cm is given as, $\frac{1}{3}\times\frac{22}{7}\times (2r)^2\times h=\frac{1}{3}\times\frac{22}{7}\times 4r^2\times h$ $=\frac{1}{3}\times\frac{22}{7}\times 4\times \frac{4200}{11}=1600$ cm 3 Hence, the correct answer is 1600 cm 3 .
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