Asked by Pinkhearts4you
Suppose a sphere, cylinder, and cone all share the same radius. The cylinder and cone also share the same height, which is twice the radius. Which of the following is true about the relationship between the volume formulas for the sphere, cylinder, and cone? (1 point)
O cone = sphere - cylincer
O cytin * der = sphere - cone
O sphere = cylin * der + cone
O cone = cylin * der - sphere
O cone = sphere - cylincer
O cytin * der = sphere - cone
O sphere = cylin * der + cone
O cone = cylin * der - sphere
Answers
Answered by
Damon
sphere Vs = (4/3) pi r^3
cylinder Vc = 2 r * pi r^2 = 2 pi r^3
cone Vco = (1/3) Vc = (2/3) pi r^3
so Vs + Vco = (4/3) pi r^3 + (2/3) pi r^3 = 2 pi r^3 which is in fact Vcylinder
So
Vcone = Vcylinder - Vsphere
cylinder Vc = 2 r * pi r^2 = 2 pi r^3
cone Vco = (1/3) Vc = (2/3) pi r^3
so Vs + Vco = (4/3) pi r^3 + (2/3) pi r^3 = 2 pi r^3 which is in fact Vcylinder
So
Vcone = Vcylinder - Vsphere
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