Volume of a cone and cylinder
The height of the cone is 4 inches
Step-by-step explanation:
The volume of cylinder = [tex]\pi * r^{2} * h\\[/tex]
The volume of cone = [tex]1/3 * \pi * r^{2} * h\\[/tex]
Value of [tex]\pi[/tex]= 3.14
In case of cylinder the value of radius r = 2 inches and height = 3 inches
Therefore, the volume of the cylinder is given by:
V1 = [tex]\pi * r^{2} * h\\[/tex] = ---------------------------( 1 )
⇒ V1= 3.14 ×2 ×2 ×3
⇒V1 = 3.14 ×12
⇒V1 =37.68 cubic inch
Volume of cone V2 = [tex]1/3 * \pi * r^{2} * h\\[/tex] --------------------------------------( 2)
V2 = 1/3 ×3.14 ×3 ×3 ×h as r =3 inches
Also, given that the volume of cylinder V1 is equal to volume of cone V2 V1 = V2
So equating equation (1) with equation (2 )
So
1/3 ×3.14 ×3 ×3 ×h = 37.68
⇒3.14 ×3 ×h = 37.68
⇒h = 37.68 / ( 3 × 3.14)
⇒ h = 4
Hence, the height of the cone is 4 inches
