Respuesta :
Answer:
1.5 inch
Step-by-step explanation:
The existing cones have a radius of 2 inches and a height of 6 inches.
Since the new cones is to have the same volume as the existing cones, we determine first the volume of the existing cone.
Volume of a Cone = [tex]\frac{1}{3}\pi r^2 h[/tex]
For the existing cone, Radius, r =2 inches, Height, h= 6 inches
Volume of the existing cone = [tex]\frac{1}{3}\pi X 2^2 X 6 =8 \pi[/tex] cubic inch
Recall, Volume of the new cones = Volume of the Existing Cone
Radius, r of the new cone = 4 inches
Volume of the new cones= [tex]\frac{1}{3}\pi r^2 h[/tex]
[tex]8 \pi=\frac{1}{3}X \pi X 4^2 X h[/tex]
[tex]8 \pi=\frac{16h\pi}{3}[/tex]
Dividing both sides by [tex]\pi[/tex]
[tex]8=\frac{16h}{3}[/tex]
To solve for the height, h, multiply both sides by [tex]\frac{3}{16}[/tex]
[tex]8 X \frac{3}{16} =\frac{16h}{3} X \frac{3}{16} \\h= 8 X \frac{3}{16} =1.5 inch[/tex]
The height of the new cone will be 1.5 inch.
