the height of a cone is 5m and its base has a radius of 9m. calculate the volume of the cone. give your answer in terms of pi

That is assuming you are talking about perpendicular height.

Yes.  I think it is conventional to assume perpendicular height is meant if the word "height" is used on  its own.  If slant height is meant then both those words would be used. 

The volume of a cone is (1/3)pi.r²h where r is radius and h is height, so: volume = (1/3)*pi*9²*5 m³

or volume = 135*pi m³

Thanks Alan,

That is assuming you are talking about perpendicular height. 

It wasn't a criticism Alan.  It is just that the students often forget, or get confused, so I like to remind them.  That is all.