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ICSE Class 10 Mathematics Question 22 of 28

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22
Question

Question 71

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

Given,

Diameter of container = 14 cm

Radius (R) = Diameter2=142\dfrac{\text{Diameter}}{2} = \dfrac{14}{2} = 7 cm

Height of container (H) = 16 cm

Diameter of rasgulla = 6 cm

Radius of rasgulla (r) = Diameter2=62\dfrac{\text{Diameter}}{2} = \dfrac{6}{2} = 3 cm

Volume of container = Volume of rasgullas + Volume of liquid

⇒ πR2H = 20×4320 \times \dfrac{4}{3} πr3 + Volume of liquid

⇒ Volume of liquid = πR2H - 803\dfrac{80}{3} πr3

⇒ Volume of liquid = π(R2H - 803r3\dfrac{80}{3}r^3)

⇒ Volume of liquid = 3.14 × (72 × 16 - 803×33\dfrac{80}{3} \times 3^3)

⇒ Volume of liquid = 3.14 × (784 - 720)

⇒ Volume of liquid = 3.14 × 64

⇒ Volume of liquid = 200.96 cm3.

Hence, volume of sweetened liquid in the container = 200.96 cm3.