A hemispherical bowl is 18cm in diameter and contains water to a depth of 7cm when level. How far can the bowl roll before the water pours out?

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1 Answer
Somebody N.
Apr 20, 2018

color(blue)(2.02) cm.

Explanation:

From the diagram we can see that the bowl needs to move the distance bb(ab) along the arc. We therefore need to find the length of this arc. We can do this if we can find the angle bbx

Using the sine function:

sin(x)=h/r

The diameter of the bowl is 18, so radius is 9.

Level of water is 7.

h=9-7=2

:.

sin(x)=2/9

x=arcsin(2/9)

Arc length is given by:

rtheta

:.

ab=9arcsin(2/9)=2.02color(white)() cm color(white)(8888) 2 d.p.

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