Question : A right circular cone is 3.6 cm high, and the radius of its base is 1.6 cm. It is melted and recast into a right circular cone with a radius of 1.2 cm at its base. Then the height of the cone (in cm) is:
Option 1: 3.6
Option 2: 4.8
Option 3: 6.4
Option 4: 7.2
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Correct Answer: 6.4
Solution :
Given: $r_1$ = 1.6 cm
$h_1$ = 3.6 cm
$r_2$ = 1.2 cm
$h_2$ is unknown (height of the second cone)
According to the question,
Volume of 1
st
cone = Volume of 2
nd
cone
⇒ ${\frac{1}{3} \pi r_1^2 h_1}={\frac{1}{3} \pi r_2^2 h_2}$
⇒ 1.6 × 1.6 × 3.6 = 1.2 × 1.2 × $h_2$
$\therefore h_2$ = 6.4
Hence, the correct answer is 6.4.
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