Question

a half circle bowl is filled completly with oil, then the oil is poured completly into the cylindrical bottle. Find the oil's height in the bottle. (The diameter of half circle bowl is 10 cm same with the diameter of the bottle)

Answer 1

Answer:

Height of oil in bottle =  $\frac{10}{3}cm$ .

Step-by-step explanation:

By half-circle bowl, I am gonna assume that you mean to say a hemispherical bowl. Well, volume of a hemisphere is given by :

$V = \frac{2}{3} *\pi *r^3$

But the value of r has been provided, i.e,

$r = \frac{d}{2} = \frac{10cm}{2} = 5cm$

Therefore, volume of the oil in the bowl is,

$V = \frac{2}{3} *\pi *5^3 = \frac{250*\pi }{3} cm^3$

Since the volume won't be altered on transferring the oil from the bowl to the bottle, the volume of oil in bottle must be the same, but volume of bottle is given by,

$V = \pi *R^2*h = \frac{250*\pi}{3} -----(R=5cm) \\h = \frac{1}{\pi*5^2}*\frac{250*pi}{3} = \frac{250}{5^{2}*3 } \\\\h = \frac{10}{3} cm$

Therefore, the height of oil in the bottle is $\frac{10}{3}cm$ .