Question

A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into
cylindrical shaped bottles each of radius 1.5 cm and height 4 cm. How many bottles are
needed to empty the bowl?

Answer 1

radius of hemisphere= 9 cm

volume of hemisphere= 2/3 π r3

= 2/3 x9x9x9 π

= 486 π 

radius of cylindrical shaped bottles= 3/2 cm

height= 4 cm

volume of bottles= π r2h

= 3/2x 3/2 x 4 π

=9 π

now,

Reaquired no. of bottles= volume of hemisphere/ volume of bottles

.  =486 π/9π

.  =54

Hence, no. of bottles required to empty the bowl = 54

Answer 2

Answer:

54 cylindrical bottles are necessary to empty a hemispherical bowl.

Step-by-step explanation:

Given :  

Internal radius of the hemispherical bowl , R = 9 cm

Diameter of the cylindrical bottle = 3 cm

Radius of the cylindrical bottle , r = 3/2 cm = 1.5 cm

Height of the cylindrical bottle , h = 4 cm

Number of cylindrical shaped bottles required to empty a hemispherical bowl , n = Volume of hemispherical bowl / Volume of each cylindrical shaped bottles

= 2/3 × πR³ /  πr²h

= 2/3 × 9³ / 1.5² × 4

= 2/3 × 729 / 2.25 × 4  

= 2 × 243 / 2.25 × 4

= 243 / 2.25 × 2  

= 243/ 4.5 = 2430/45 = 54  

n = 54

Hence, 54 cylindrical bottles are required to empty a hemispherical bowl.

HOPE THIS ANSWER WILL HELP YOU…..