Discussion

Explanation:

Total volume of the bottle = Volume of top cylinder + Volume of frustum + Volume of bottom cylinder

Now,

Volume of top cylinder = π × r2 × h = 22/7 × 32 × 7 = 198 cm2.

Volume of bottom cylinder = π × r2 × h = 22/7 × 62 × 7 = 792 cm2.

Now, for the frustum of the cone, BCED,

∆ADE ~ ∆ABC
∴ AX : AY = DE : BC = 3 : 6 = 1 : 2
⇒ AX = 7 and AY = 14

​​​​​​​

Volume of frustum = Volume of bigger cone (ABC) - Volume of smaller cone (ADE)
                              = 1/3 × π × R2 × h - 1/3 × π × r2 × h
                              = 1/3 × 22/7 × 62 × 14 - 1/3 × 22/7 × 32 × 7
                              = 528 - 66
                              = 462

∴ Total volume of the bottle = 198 + 792 + 462 = 1452 cm2.

Hence, option (b).

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