Question

a cylindrical vessel of height 24cm and diameter 40cm is full of water. find the exact number of small cylindrical bottles,each of height 10cm and diameter 8cm which can be filled with this water.

Answer 1

Cylinder has height =24cm
Daimeter=40cm
Radius=20cm

Vol of cylinder=πr^2h
=π(20)^2*24
=30159.29cm sq
Now
Height of bottle =10cm
Diameter=8cm
Radius=4cm
So,
Vol of each bottle =π(4)^2*10
=502.65cm sq
Therefore
No. of bottles=(30159.29) / (502.65)
=60.0006
=60 bottles.

Answer 2

According to question,

Volume of cylindrical vessel = Volume of cylindrical bottles × No of bottles.

                                      πR²H = πr²h × No of Bottles.
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Where R = 20 cm    H = 24 cm

            r  =  4 cm      h = 10 cm
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Cancelling π on both sides as it is common, Then

                     R²H = r²h  ×  No of bottles.

            (20)² × 24 = (4)² × 10  ×  No of Bottles.

       No of Bottles = 20 × 20 × 24 / 4 × 4 × 10 

       No of Bottles = 60 bottles.
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