Dig out your formulas for volume of cylinder and cone:
cylinder V=Bh = pi * r^2 * h = 160pi
cone: V = 1/3Bh = 1/3 pi r^2 * h = 2/3 pi
SO, 160/(2/3) = 240 cones.
cylinder V=Bh = pi * r^2 * h = 160pi
cone: V = 1/3Bh = 1/3 pi r^2 * h = 2/3 pi
SO, 160/(2/3) = 240 cones.
First, let's find the volume of the metal cylinder using the formula for the volume of a cylinder: V = πr^2h, where V is the volume, r is the radius, and h is the altitude.
Given:
Radius of the metal cylinder (r) = 4 inches
Altitude of the metal cylinder (h) = 10 inches
Volume of the metal cylinder (V) = π(4^2)(10) = 160π cubic inches
Next, let's find the volume of each cone using the formula for the volume of a cone: V = (1/3)Ï€r^2h, where V is the volume, r is the radius, and h is the altitude.
Given:
Radius of each cone (r) = 1 inch
Altitude of each cone (h) = 2 inches
Volume of each cone (V) = (1/3)Ï€(1^2)(2) = (2/3)Ï€ cubic inches
Finally, to find the number of cones formed, we will divide the volume of the metal cylinder by the volume of each cone:
Number of cones = (Volume of metal cylinder)/(Volume of each cone)
= (160Ï€)/((2/3)Ï€)
= (160Ï€)(3/2Ï€)
= 240
Therefore, the number of cones formed is 240.