Math, asked by lamgirl, 7 months ago

A juice seller was serving his customers using glasses
as shown in the figure. The inner diameter of the
cylindrical glass was 5 cm, but the 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 capacity of the glass and its
actual capacity. [Use t = 3.14.] ​

Answers

Answered by Anonymous
87

Given :-

  • Radius of the cylindrical glass,r = \frac{5}{2} \\
  • Height of the cylindrical glass = 10cm
  • Radius of the hemisphere part,r =  \frac{5}{2} \\

To find :-

  • capacity of the glass

solution :-

Apparent capacity of the glass

\sf \longrightarrow volume \: of \: the \: cylinder \\  = \pi {r}^{2} h \\

  \sf \longrightarrow = (3.14 \times  \frac{5}{2}  \times  \frac{5}{2}  \times 10) {cm}^{3} \\

 \sf \longrightarrow volume \: of \: hemspherical \: part \\  =  \frac{2}{3} \pi {r}^{3}  \\

 \longrightarrow \sf ( \frac{2}{3}  \times 3.14 \times  \frac{5}{2}  \times  \frac{5}{2}  \times  \frac{5}{2} ) {cm}^{3}  \\

 \longrightarrow \sf ( \frac{196.25}{6})  {cm}^{3}  \\  = 32.71 {cm}^{3}

therefore, actual capacity of the glass = apparent capacity of the glass - volume of the hemspherical part

= (196.25 - 32.71)cm³

= 163.54 cm³

hence, the capacity of the glass is 163.54 cm³.

_______________

NoTe :-

  • refer the above attachment
Attachments:
Answered by nk6452
3

Actual capacity of Glass= Volume of cylinder - Volume of hemisphere

⇒ volume of cylinder=πr2h

where r=2D=25cm;

h=10cm;D=3.14

⇒3.14×(25)2×10

⇒3.14×6.25×10

⇒196.25cm3

Volume of Hemisphere ⇒32πr3 

(r=25)

⇒32×3.14×(25)3

⇒32×3.14×15.625

⇒32.7cm3

∴ Actual capacity 196.25−32.7=163.55cm3

and apparent capacity ⇒196.25cm3

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