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 ?

Answer 1

Radius of hemispherical bowl = 9 cm

Volume of liquid in the bowl = $\frac{2}{3}\pi r^3=(\frac{2}{3}\pi \times 9\times 9\times 9)=486\pi c{m}^3$

Radius of each cylindrical bottle = $\frac{3}{2}cm$

And, height = $4cm$

Volume of each cylindrical bottle = $\pi R^{2}h=\pi \times \frac{3}{2}\times \frac{3}{2}\times 4=9\pi c{m}^3$

Therefore, required number of bottles = $\frac{486\pi }{9\pi }=54$