The innder 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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Solution

Volume that can hold = volume of cylinder vessel - volume of hemisphere

radius of the cylinder = radius of hemisphere = 7 cm

$∴ V o l u m e t h a t c a n h o l d = v o l u m e o f c y l i n d e r v e s s e l - v o l u m e o f h e m i s p h e r e$

= $π \times 7^{2} \times 16 - \frac{2}{3} \times π 7^{3}$
= [ $π \times 7^{2}] [16 - \frac{14}{3})$ ]
=[ $\frac{22}{7} \times 7^{2}$ ] [ $\frac{48 - 14}{3}$ ] = [ $\frac{22 \times 7 \times 34}{3}$ ]

= $\frac{5236}{3}$

= 1743.33 $c m^{3}$

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The innder 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.

Volume that can hold = volume of cylinder vessel - volume of hemisphere radius of the cylinder = radius of hemisphere = 7 cm ∴Volumethatcanhold=volumeofcylindervessel−volumeofhemisphere = π×72×16−23×π 73 = [ π×72][16−143) ] =[227×72] [48−143] = [22×7×343] = 52363 = 1743.33 cm3