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  • A juice seller was serving his customers using glasses as shown in Figure 3. The inner diameter of the cylindrical glass was  but bottom of the glass had a hemisp

A juice seller was serving his customers using glasses as shown in Figure 3. The inner diameter of the cylindrical glass was 5cm but bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was 10\; cm, find the apparent and actual capacity of the glass. (use\; \pi =3.14)

 

 

 
 
 
 
 

Answers (1)

Given, the height of the glass =10\; cm

radius of glass =\frac{5}{2}\; cm=2.5\; cm

To find = Volume of the shaded region/glass

\Rightarrow vol. of glass = [ Vol. of the cylinder - Vol. of homisphere]

                          =\pi \times r^{2}h-\frac{2}{3}\pi r^{3}

                        =\pi r^{2}\left [ h-\frac{2}{3} r\right ]

                       =\frac{22}{7}\times \left ( \frac{5}{2} \right )^{2}\left [ 10-\frac{5}{3} \right ]

                        =\frac{22\times 25}{7\times 4}\times \frac{25}{3}=\frac{6875}{42}

\Rightarrow Vol. \; of\; glass =163.7\; cm^{3}=actual\ capacity

Apparent capacity = volume of the cylindrical portion

volume\ of\ cylinder=\frac{22}{7}\times \left ( \frac{5}{2} \right )^2\times10\\=196.34cm^3

Posted by

Safeer PP

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