A shot – put made of iron
A shot – put made of iron with a diameter of 12 cm is melted into a solid cylinder with a height of 2 cm. What is the diameter of the cylinder made?
12 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
24 cm
Volume of sphere = $ \frac{4}{3}\pi r^3 $
Diameter of sphere = $ 12 \text{ cm} r = 6 \text{ cm} $
Volume of sphere = $ \frac{4}{3}\pi (6)^3 = \frac{4}{3}\pi \times 216 = 288\pi \text{ cm}^3 $
Volume of cylinder = $ \pi R^2 h $
Height of cylinder h = $ 2 \text{ cm} $
Since volume is conserved:
$ \pi R^2 \times 2 = 288\pi $
$ 2R^2 = 288 $
$ R^2 = 144 $
R = 12 cm
Diameter of cylinder = 2R = 24cm
Answer = 24 cm
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