Samriddh has a solid metal ball with a diameter of 9 cm. He melts it and uses the material to make a solid cylinder. If the diameter of the cylinder is the same as that of the ball, find the height of the cylinder.
Samriddh has a solid metal ball with a diameter of 9 cm. He melts it and uses the material to make a solid cylinder. If the diameter of the cylinder is the same as that of the ball, find the height of the cylinder.
समृद्ध के पास धातु की एक ठोस गेंद है, जिसका व्यास 9 cm है। वह इसे पिघलाता है और इस सामग्री का उपयोग करके एक ठोस बेलन बनाता है। यदि बेलन का व्यास, गेंद के व्यास के समान है, तो बेलन की ऊँचाई ज्ञात कीजिए।
Detailed Solution & Logic
6 cm
Diameter of ball = 9 cm r = \(\dfrac{9}{2} = 4.5\) cm
Diameter of cylinder = 9 cm R = 4.5 cm
Let height of cylinder = h
Volume of sphere = \(\dfrac{4}{3}\pi r^3 = \dfrac{4}{3}\pi (4.5)^3 = 121.5 \pi\ \text{cm}^3\)
Volume of cylinder = \pi R^2 h = \pi (4.5)^2 h = 20.25 \pi \cdot h \)
Equating volumes:
$ 121.5 \pi = 20.25 \pi \cdot h $
$ h = \dfrac{121.5}{20.25} = 6 $
Answer = h = 6cm
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