Question

A hemispheric bowl of cereal internal radius 9 cm contain a liquid. This liquid has to be filled in cylindrical shape small bottle of diameter 3 cm and height 4 cm . How many bottles are required to empty the bowl?

Answer 1

GIVEN :-

• Radius of hemispheric bowl = 9 cm

• Diameter of the cylindrical bottle  = 3 cm

        ∴ Radius of the cylindrical bottle = 1.5 cm

• Height of the cylindrical bottle = 4 cm

TO FIND :-

• The number of bottles are required to empty the bowl.

SOLUTION :-

Let the number of bottles be x .

$\boxed{\bf Volume \ of \ hemisphere = \dfrac{2}{3} \pi r^3 }$

$\longrightarrow \sf Volume \ of \ hemispherical \ bowl = \dfrac{2}{3}\times\pi \times 9 \times 9 \times 9$

                                                    $= \sf 2 \times \pi \times 3 \times 9 \times 9 \\\\= 486 \pi$

$\boxed{\bf Volume \ of \ cylinder = \pi r ^2 h}$

$\longrightarrow\sf Volume \ of \ one \ cylindrical \ bottle = \pi \times 1.5 \times 1.5 \times 4$

                                                      $= \sf 9 \pi$

According to the question,

Volume of hemispherical bowl = x × Volume of one cylindrical bottle

$\longrightarrow\sf 486 \pi = x \times 9 \pi \\\\\longrightarrow x = \dfrac{486\pi}{9\pi} \\\\\longrightarrow x=\dfrac{486}{9} \\\\\longrightarrow \bf x = 54$

Number of bottles required to empty the bowl = 54