Question

a hemispherical bowl of radius of 9cm contains a liquid.this liquid is to be filled into cylindrical small bottles of diameter 3cm and height 4cm.how many bottles will be need to empty the bowl

Answer 1

Answer:

54 bottles will be needed to empty the bow

Step-by-step explanation:

$\frac{Volume(bowl)}{Volume(bottle)} = No.(bottles)$===(i)

Vol. of bowl

Volume of hemisphere =

$\frac{2}{3} \pi r^3\\\\= (\frac{2}{3})( \frac{22}{7} )(9)(9)(9)\\\\= \frac{(44)(3)(9)(9)}{7} \\\\=\frac{10692}{7} cm^3$

Vol. of bottle

Volume of cylinder = πr²h

$=\frac{22}{7} (1.5)(1.5)(4)\\\\=\frac{(22)(2.25)(4)}{7} \\\\= \frac{198}{7}$

Using (i), thus number of bottles =

$\frac{10692}{7}$÷ $\frac{198}{7}$

$=(\frac{10692}{7} )(\frac{7}{198})\\\\=\frac{10692}{198}\\\\= 54$

Hence 54 bottles will be needed to empty the bowl