Question

A famous sweet shop “Madanlal Sweets” sells tinned rasgullas. The tin container is cylindrical in shape with diameter 14 cm, height 16 cm, and it can hold 20 spherical rasgullas of diameter 6 cm and sweetened liquid such that the can is filled and then sealed. Find out how much sweetened liquid the can contains. Take π = 3.14.

Answer 1

Given: A cylindrical tin: diameter = 14 cm, height = 16 cm. It contains 20 spherical rasgullas, each of diameter = 6 cm. Find volume of sweetened liquid. Take π = 3.14.

Step-wise calculation:

1. Cylinder radius r_cyl = `14/2` = 7 cm.

Volume of cylinder: V_cyl = πr_cyl²h

= 3.14 × 7² × 16 

7² = 49

49 × 16 = 784

V_cyl = 3.14 × 784

= 2461.76 cm³

2. Rasgulla (sphere) radius r_sph = `6/2` = 3 cm.

Volume of one sphere: V_sph = `4/3` πr_sph³

= `4/3 xx 3.14 xx 3^3`

3³ = 27

3.14 × 27 = 84.78

V_sph = `4/3 xx 84.78`

= 113.04 cm³

3. Volume of 20 rasgullas:

V₂₀ = 20 × 113.04

= 2260.80 cm³

4. Volume of sweetened liquid = V_cyl – V₂₀:

= 2461.76 – 2260.80

= 200.96 cm³

The can contains 200.96 cm³ of sweetened liquid = 201.0 cm³.