Answer: The height of the cone is 8.6 cm.
Step-by-step explanation:
We know that the volume of cone is given by :-
[tex]\text{Volume }=\dfrac{1}{3}\pi r^2h[/tex] , where r= radius and h is height
Given : Volume of cone = 225 cm³
Base length = 10 cm
i.e. radius = [tex]\dfrac{10}{2}=5 \ cm[/tex] [cone has circular base]
Substitute these values in formula , we get
[tex]225=\dfrac{1}{3}(3.14)(5)^2(h)\\\\\Rightarrow\ h=\dfrac{225\times3}{3.14\times25}=8.59872611465\approx8.6[/tex]
Hence, the height of the cone is 8.6 cm.
