Respuesta :
The height of the cone is inches, if the cylinder and cone have the same volume.The cylinder has a radius of 2 inches and a height of 3 inches. The cone has a radius of 3 inches.
Step-by-step explanation:
The given is,
A cylinder and a cone have the same volume
Cylinder has a radius 2 inches and height of 3 inches.
Cone has a radius of 3 inches
Step:1
For Cylinder'
Formula to calculate the volume of cylinder is,
[tex]V = \pi r^{2} h[/tex]..................................................(1)
where,
r - 2 inches
h - 3 inches
From the equation (1)
= [tex]\pi[/tex] × [tex]2^{2}[/tex] × 3
= 37.70
V = 37.70 cubic inches
Step:2
For cone,
Formula to calculate the volume of cone is,
[tex]V = \pi r^{2} \frac{h}{3}[/tex]..................................................(2)
From the statement,
cylinder and a cone have the same volume
[tex]V_{cylinder}[/tex] = [tex]V_{cone}[/tex]
37.70 = [tex]\pi[/tex] × [tex]3^{2}[/tex] × [tex]\frac{h}{3}[/tex]
37.70 = 9.42478 × h
Height of the cone, h = 4 inches
Result:
Thus the height of the cone is 4 inches, if a cylinder and cone have the same volume.The cylinder has a radius of 2 inches and a height of 3 inches. The cone has a radius of 3 inches.
