Answer:
60 cubic meters will be the volume of such cone.
Step-by-step explanation:
Formula for volume of a cylinder:
[tex]V = \pi r^{2} h ...... (1)[/tex]
Where [tex]r[/tex] is the radius of base of cylinder
and [tex]h[/tex] is the height of cylinder
V = 180 cubic meters
Formula for volume of a cone:
[tex]V' = \dfrac{1}{3}\pi R^{2} H ...... (2)[/tex]
Where [tex]R[/tex] is the radius of base of cone
and [tex]H[/tex] is the height of cone
Now, it is given that height and radius of cone are equal.
[tex]r = R\\h =H[/tex]
Putting the values in equation (2):
[tex]V' = \dfrac{1}{3}\pi r^{2} h[/tex]
Using equation (1):
[tex]V' = \dfrac{1}{3} \times V[/tex]
Putting V = 180 cubic meters
[tex]\Rightarrow V' = \dfrac{1}{3} \times 180\\\Rightarrow V'=60 \text { cubic meters}[/tex]
Hence, 60 cubic meters will be the volume of such cone.
