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# The inner diameter of a glass is 7 cm and it has a raised portion in the bottom in the shape of a hemisphere, as shown in the figure. If the height of the glass is 16 cm, find the apparent capacity and the actual capacity of the glass

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In the given problem shape of solid is cylinder. To find answer of this problem use cylinder volume formula. problem number 31 from RS Aggarwal book, chapter volume and surface area of solid, page number 289.

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1. We have,

The height of the glass, h = 16 cm

the base radius of cylinder = the base radius of hemisphere

r =7/2

Now,

The apparent capacity of the glass = Volume of the cylinder – Volume of the hemisphere

= πr²h – [2/3]πr³

= πr² ( h – ([2/3]r) )

= [22/7][3.5]² ( 16 – ([2/3] 3.5) )

= 526.18 cm³

∴ The apparent capacity of the glass is 526.18 cm³

and

actual capacity of the glass = Volume of the cylinder

∴ actual capacity of the glass = πr²h

= [22/7] * [3.5]² * 16

= 616 cm²

∴ actual capacity of the glass is 616 cm²

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