A cylinder and hemisphere have the same radius. Their combined height is 30 cm.
A cylinder and hemisphere have the same radius. Their combined height is 30 cm. if the cylinder and hemisphere have equal Volumes, find the radius.
एक बेलन और एक अर्धगोले की त्रिज्या समान है। उनकी संयुक्त ऊँचाई 30 सेमी है। यदि बेलन और अर्धगोले का आयतन समान है, तो त्रिज्या ज्ञात कीजिए।
Detailed Solution & Logic
Correct Answer:
18 cm/ 18 सेमी
मान लीजिए समान त्रिज्या = r सेमी।
बेलन की ऊँचाई
= 30 - r
बेलन का आयतन
$\pi r^2(30 - r)$
अर्धगोले का आयतन
$\frac{2}{3}\pi r^3$
प्रश्नानुसार,
$\pi r^2(30 - r) = \frac{2}{3}\pi r^3$
$30 - r = \frac{2}{3}r$
90 - 3r = 2r
90 = 5r
r = 18
सही उत्तर: 18 सेमी
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