A shot-put iron sphere of diameter 2 cm is melted and cast into a solid cylinder of height 2 cm. What will be the diameter of the cylinder thus made?
A shot-put iron sphere of diameter 2 cm is melted and cast into a solid cylinder of height 2 cm. What will be the diameter of the cylinder thus made?
2 cm व्यास वाले लोहे से बने एक गोले (shot-put) को पिघलाकर 2 cm ऊंचाई वाला एक ठोस बेलन में ढाला जाता हैं इस प्रकार बने बेलन का व्यास क्या होगा?
Detailed Solution & Logic
Correct Answer:
24 cm
Sphere radius = $6$ cm
Sphere volume:
$V = \frac{4}{3}\pi r^3$
$= \frac{4}{3}\pi (6)^3$
$= 288\pi$
Cylinder height = $2$ cm
Let cylinder radius = $R$
Cylinder volume:
$V = \pi R^2 h$
$= \pi R^2 \times 2$
$= 2\pi R^2$
Since volume remains same:
$2\pi R^2 = 288\pi$
$R^2 = 144$
$R = 12$
Diameter of cylinder = $2 \times 12 = 24$ cm
Correct answer: 24 cm
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