Question

30. At a ramzan mela, a stall keeper in one of the food stalls has a large cylindrical vessel of base radius
om filled up to a height of 32em with orange juice. The juice is filled in small cylindrical glasses of radius 3 cm upto a height of 8cm and sold for rs 3 each. How much money does the stall keeper receive
by selling the juice completely?
​

Answer 1

Answer:

Step-by-step  of explanation:

Number of Glasses Sold = Volume of juice in vessel / volume of juice in 1 glass

Volume of juice in vessel

juice in vessel is in form of cylinder with

Radius = 15cm

Height = 32 cm

Volume of juice in the vessel = πr²h

= π× 15×15×32 cm³

Volume of juice in 1 glass

juice in glass is in form of cylinder with

Radius = 3cm

Height = 8 cm

Volume of juice in the vessel= πr²h

= π ×3 × 3× 8 cm³

Number of glasses sold = Volume of juice in vessel/ Volume of juice in 1 glass

= π × 15 ×15 × 32 /π ×3× 3×8

= 5 × 5× 4

= 100

Money received by selling 1 glass = Rs .3

Money received by selling 100 glass = 3 × 100

= Rs. 300

Answer 2

Solution :-

The volume of juice in the vessel

⠀⠀⠀⠀⠀⠀= volume of cylindrical vessel

⠀⠀⠀⠀⠀⠀= π${R}^{2}$H

(where R and H are taken as the radius and height respectively)

⠀⠀⠀⠀⠀⠀= π × 15 × 15 ×32 ${cm}^{3}$

Similarly the volume of juice each glass can hold

⠀⠀⠀⠀⠀⠀= π${r}^{2}$h

( where are and H are taken as the radius and height respectively of each glass)

⠀⠀⠀⠀⠀⠀= π × 3 × 3 × 8 ${cm}^{3}$

So number of glasses of juices that are sold

⠀⠀⠀⠀⠀⠀= $\dfrac{volume\:of\:vessel}{volume\:of\:glass}$

⠀⠀⠀⠀⠀⠀= $\dfrac{π\:×\:15\:×15\:×\:32}{π\:×\:3\:×3\:×\:8}$

⠀⠀⠀⠀⠀⠀= 100

∴ amount received by the stall keeper

⠀⠀⠀⠀⠀⠀⠀⠀⠀= 15 × 100

⠀⠀⠀⠀⠀⠀⠀⠀${\boxed{\large{\bold{=\:₹1500}}}}$⠀