Question

A hemispherical bowl of internal radius 9 cm contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 3 cm and height 4 cm. How many bottles will be needed to empty the bowl?

Answer 1

According to the problom

Given that

Radius of hemispherical bowl = 9 cm

Hence the volume of bowl = $\frac{2}{3}\pi r^2$

Implies that

=$\frac{2}{3}\times \frac{22}{7}\times 9\times 9\times 9$

Implies that

=1527.42$c{m}^3$

Since height of the bottle (h) = $4cm$

and Diameter of the cylindrical bottles=$3cm$

Implies that

radius = $1.5cm$

Hence ,

the volume of the cylindrical bolltle = $\pi r^{2}h$

=$=\frac{22}{7}\times 1.5\times 1.5\times 4c{m}^3$

Let the number of bottle be (n)

Implies that

=$n\times \frac{22}{7}\times 9\times 9\times 9$

implies that

=$n=\frac{2}{3\times 1.5\times 1.5\times 4}\times 9\times 9\times 9$

implies that

n=$5$

Hence the number of bottle is $54$.