Question

A hemispherical bowl of internal radius 15 cm contains a liquid. The liquid is to be filled into cylindrical shaped bottles of diameter 5 cm and height 6 cm. The number of bottles required to empty the bowl is:

• A. 40
• B. 30
• C. 60
• D. 50

Answer 1

Answer:

C. 60

Volume of hemispherical bowl

Radius ( r = 15 ) cm

Volume of hemisphere:

$V = \frac{2}{3} \pi r^3$
$= \frac{2}{3} \pi (15)^3$
$= \frac{2}{3} \pi (3375)$
$= 2250\pi \text{ cm}^3$
Volume of one cylindrical bottle

Diameter = 5 cm
So, radius ( r = 2.5 ) cm
Height ( h = 6 ) cm

$V = \pi r^2 h$
$= \pi (2.5)^2 (6)$
$= \pi (6.25)(6)$
$= 37.5\pi \text{ cm}^3$
Number of bottles required

$\frac{2250\pi}{37.5\pi}$
$= \frac{2250}{37.5}$
$= 60$

60 bottles are required.