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

Answer 1

Volume of the hemispherical bowl
= {(4/3)πr^2}÷2
= {(4×9×9)/(3×2)} π
= 54π cubic cm

Volume of cylinder
= πr^2h/3
= ((3/2)^2×4/3)π
= 3π cm^3

Number of cylindrical bottles needed to empty the bowl
= 54π/3π
= 18 Bottles

Answer 2

$\underline \bold{Solution:-}$

Internal radius of hemispherical bowl (R) = 9 cm

Volume of hemispherical bowl

$= \frac{2}{3} \pi {r}^{3} \\ \\ = \frac{2}{3} \pi( {9)}^{3} \\ \\ = 486\pi \: {cm}^{3}$

Height of bottles (h) = 4 cm

Radius of bottles (r) = 3/2 = 1.5 cm

Volume of cylindrical bottles

$= \pi {r}^{2} h \\ \\ = \pi \times {1.5}^{2} \times4 \\ \\ = \pi \times 2.25 \times 4 \\ \\ = 9\pi \: {cm}^{3}$

Number of bottles required

$= \frac{volume \: of \: hemispherical \: bowl}{volume \: of \: bottles} \\ \\ = \frac{486}{9} \\ \\ = 54\: bottles$