The radius of a hemispherical bowl is 9 , cm. | vedclass

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(A) The volume of the hemispherical bowl is given by $V_h = \frac{2}{3} \pi r^3$,where $r = 9 \, cm$.$V_h = \frac{2}{3} 	imes \pi 	imes (9)^3 = \fra

Vedclass · Accepted Answer

$54$

Vedclass · Answer

(A) The volume of the hemispherical bowl is given by $V_h = \frac{2}{3} \pi r^3$,where $r = 9 \, cm$.$V_h = \frac{2}{3} 	imes \pi 	imes (9)^3 = \frac{2}{3} 	imes \pi 	imes 729 = 486 \pi \, cm^3$.The volume of one cylindrical bottle is given by $V_c = \pi r_c^2 h$,where diameter $d = 3 \, cm$,so radius $r_c = 1.5 \, cm$ and height $h = 4 \, cm$.$V_c = \pi 	imes (1.5)^2 	imes 4 = \pi 	imes 2.25 	imes 4 = 9 \pi \, cm^3$.The number of bottles that can be filled is $n = \frac{V_h}{V_c} = \frac{486 \pi}{9 \pi} = 54$.Therefore,$54$ bottles can be filled.

The radius of a hemispherical bowl is $9 \, cm$. It is completely filled with some medicine. If this medicine is filled in cylindrical bottles of diameter $3 \, cm$ and height $4 \, cm$,how many bottles can be filled?

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