Question

A hemispherical bowl of internal radius 18 cm contains an edible oil to be filled in cylindrical bottles of radius 3 cm and height 9 cm. How many bottles are required to empty the bowl ?

Answer 1

Dear Student,

Answer: 48 bottles

Solution:

Volume of hemisphere =
$\frac{2}{3} \pi {r}^{3}$
radius of hemisphere is given as r = 18 cm

Volume of hemisphere =
$\frac{2}{3} \times \frac{22}{7} \times ( {18)}^{3} \\ \\ = \frac{44}{21} \times 5832 \\ \\ = 12219.43 \: \: \: \: {cm}^{3}$
Volume of cylindrical bottle =
$\pi {r}^{2} h$
radius = 3 cm

Height = 9 cm

Volume of cylindrical bottle =
$= \pi \: \times {3}^{2} \times 9$
$= \: \frac{22}{7} \times 81 \\ \\ = 254.46 \: \: {cm}^{3}$
Total number of bottles filled =
$\ \frac{(volume \: of \: cylider)}{(volume \: of \: bottle)}$
Total number of bottles filled=
$= \frac{12219.43}{254.46}$


= 48 bottles

Hope it helps you.

Answer 2

SOLUTION :

Given :

Radius of hemispherical bowl (R)= 18 cm

Radius of cylindrical bottle (r)= 3 cm

Height of the bottle (h) = 9 cm

Let the number of bottles required to empty the bowl = x

Volume of x cylindrical bottles = volume of the hemispherical bowl

x × πr²h = 2/3πR³

x × r²h = ⅔ × R³

x × 3×3 × 9 = ⅔ × 18 × 18 × 18

x = (2 × 18 × 18 × 18) / (3 × 3×3 × 9)

x = 2× 2 × 6 × 2 = 48

x = 48

Hence, 48 bottles are required to empty the bowl .

HOPE THIS ANSWER WILL HELP YOU..