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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