Uncle Bert was making porridge in a cylindrical pan of diameter 24cm. The spoon he was using is 26 cm long. It accidentally falls and sinks into the porridge. Calculate the minimum volume of porridge necessary to hide the spoon. You may ignore the volume of the spoon.
aptitude - Steve, Thursday, May 9, 2013 at 4:19pm
26^2-24^2 = 100
So, the porridge must be at least 10 cm deep.
The volume of porridge is thus at least 1440π = 4523.9 cm^3
aptitude - amit sharma, Thursday, May 9, 2013 at 4:24pm
hw did u get dis ??
The volume of porridge is thus at least 1440π
aptitude - Steve, Thursday, May 9, 2013 at 4:36pm
volume of a cylinder v = πr^2 h
They wouldn't be asking this kind of question if you hadn't learned that.
Now, how did I get a depth of 10 cm?
Draw a diagram of the pot and spoon, as seen from the side. The spoon is lying with one end on the bottom of the pot, and the other end leaning against the side of the pot.
Recall the Pythagorean Theorem. You have a right triangle with the spoon forming the hypotenuse, and the diameter of the bottom of the pot forming one leg. If the depth is d,
24^2 + d^2 = 26^2
Whenever you get one of these problems, it always pays to draw a diagram, and review what you have studied so far. The answer will come from using the topics covered; these are not just random problems pulled out of a hat.