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
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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