Question

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 the each bottle if 10 % liquid is waste in this transfer

Answer 1

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Answer 2

Answer:

Height of each bottle is 5.4 cm.

Step-by-step explanation:

Given : A hemispherical bowl of internal diameter 36 cm contains liquid this liquid is filled into 72 cylindrical bottles of diameter 6 cm

To find: The height of the each bottle if 10 % liquid is waste in this transfer?

Solution :

Internal diameter of hemisphere bowl=36 cm

Internal radius of hemisphere bowl=18 cm

Volume of the liquid in the bowl

$V=\frac{2}{3}\pi r^3$

$V=\frac{2}{3}\pi 18^3$

$V=\frac{2}{3}\pi (5832)$

$V=3888\pi cm^3$

Diameter of the bottle =6 cm

Radius of the bottle = 3 cm

Let height be h

Volume of each bottle $v=\pi r^2 h$

$v=\pi 3^2 h$

$v=9\pi h$

Liquid in the bowl is filled into 72 bottles,

10 % liquid is waste in this transfer

∴ 90% of volume of liquid in the bowl = 72× volume of liquid in each bottle

$\frac{90}{100} \times 3888\pi=72\times 9\pi h$

$3499.2=648 h$

$h=\frac{3499.2}{648}$

$h=5.4 cm$

Therefore, Height of each bottle is 5.4 cm.