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प्रश्न
A cylindrical vessel having diameter equal to its height is full of water which is poured into two identical cylindrical vessels with diameter 42cm and height 21cm which are filled completely. Find the diameter of cylindrical vessel?
उत्तर
Given that diameter is equal to height of a cylinder
so h = 2π
Volume of cylinder=πr2h
So volume = πr2(2r)
2πr3
Volume of each vessel =πr2h
Diameter = 42cm
Height = 21cm
Diameter(d) = 2r
2r = 42
r = 21
∴ Radius = 21cm
Volume of vessel = π(21)2x21 ...........(2)
Since volumes are equal
Equating (1) and (2)
⇒ 2πr3= π(21)2 x 21 x 2 (∵ 2 identical vessels)
⇒ `r^2=(pi(21)^2xx21xx2)/(2xxpi)`
⇒ r3 = (21)3
⇒ r = 21 ⇒ d = 42cm
∴ Radius of cylindrical vessel = 21cm
Diameter of cylindrical vessel= 42 cm.
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