Question

A hemispherical bowl has internal diameter 36cm contains a liquid . This is liquid is to be filled in the cylindrical bottles of radius 3 cm and height 6 cm how many bottles are required to empty the bowl

Answer 1

internal diameter=36cm
internal radius=36/2=18cm
volume of bowl=2/3 πr³
=2/3(22/7)(18³)
=2×22×18³/7×3
=12219.4cm³
volume of bottle=πR²h
=22/7(3²)(6)
=22×9×6/7
=169.7cm³
no. of bottles required=12219.4/169.7
=72.23=72

Answer 2

$\underline \bold{Solution:-}$

Internal radius of hemispherical bowl (R) = 18 cm

Volume of hemispherical bowl

$= \frac{2}{3} \pi {r}^{3} \\ \\ = \frac{2}{3} \pi( {18)}^{3} \\ \\ = 3888\pi \: {cm}^{3}$

Height of bottles (h) = 6 cm

Radius of bottles (r) = 3 cm

Volume of cylindrical bottles

$= \pi {r}^{2} h \\ \\ = \pi \times {3}^{2} \times 6 \\ \\ = \pi \times 9 \times 6 \\ \\ = 54\pi \: {cm}^{3}$

Number of bottles required

$= \frac{volume \: of \: hemispherical \: bowl}{volume \: of \: bottles} \\ \\ = \frac{3888}{54} \\ \\ = 72 \: bottles$