Question

A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped small bottles, each of diameter 3 cm and height 4 cm. How many bottles are needed to empty the bowl?

• A. 54
• B. 27
• C. 36
• D. 18

Answer 1

The correct option is A

54

Radius of hemispherical bowl$=9cm$
Volume of liquid in the bowl$=\frac{2}{3}\pi r^3$
$=(\frac{2}{3}\pi \times 9\times 9\times 9)c{m}^3=486\pi c{m}^3$
Radius of each cylindrical bottle$=\frac{3}{2}cm$ and its height $=4cm$
Volume of each cylindrical bottle$=\pi R^{2}h=(\pi \times \frac{3}{2}\times \frac{3}{2}\times 4)c{m}^3=9\pi c{m}^3$
Required number of bottles$=\frac{Volumeofbowl}{Volumeofbottle}=\left(\frac{486\pi }{9\pi }\right)=54$.
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