# A hemispherical bowl of internal diameter 36 cm contains liquid. This liquid is filled into 72 cylindrical bottles of diameter 6 cm. Find the height of each bottle, if 10% liquid is wasted in this transfer. - Mathematics

A hemispherical bowl of internal diameter 36 cm contains liquid. This liquid is filled into 72 cylindrical bottles of diameter 6 cm. Find the height of each bottle, if 10% liquid is wasted in this transfer.

#### Solution

Internal diameter of the bowl = 36 cm
Internal radius of the bowl, r = 18 cm
Volume of the liquid, V =(2/3)𝜋r3 =(2/3)× 𝜋 × 183
Let the height of the small bottle be ‘h’.
Diameter of a small cylindrical bottle = 6 cm
Radius of a small bottle, R = 3 cm
Volume of a single bottle = 𝜋R2h = 𝜋 × 32 × h
No. of small bottles, n = 72
Volume wasted in the transfer =(10/100)×(2/3)× 𝜋 × 183
Volume of liquid to be transferred in the bottles

=2/3xxpixx18^3-10/100xx2/3xxpixx18^3

=2/3xxpixx18^3(1-10/100)

=2/3xxpixx18^3xx90/100

we know that volume of cylinder =pir^2h so we get

72(pir^2h)=(2/3xxpixx18^3xx90/100)

72=(2/3xxpixx18^3xx90/100)/(pixx3^2xxh)

72=(2/3xx18^3xx9/10)/(3^2xxh)

h=(2/3xxpixx18xx18xx18xx9/10)/(pixx3^2xx72)

h=5.4 cm
Height of the small cylindrical bottle = 5.4 cm

Concept: Surface Area of a Combination of Solids
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