Question

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.] ​

Answer 1

➝ 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

Answer 2

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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