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I call these backwards sphere problems. Given the area of a sphere, find the radius,volume, and diameter of a sphere.
Given the area of a sphere, find the radius and diameter. We are given a problem with a sphere has an area of 24 square inches and we need to find the radius and the diameter, and we will do that by using the area formula. The area formula of a sphere is equal to 4/3Pi *radius squared. I will plug in 24 for the area. 24 = 4/3Piradius squared
Next, I solve this and I will divide by four and also divide by Pi because Pi is just a constant 3.145 I will put this in my calculator. This equals 24/ (4Pi) =1.91 and this will equal my radius squared. In order to undo a square you take the square root. The square root of 1.91 equals 1.38 which becomes my radius. I will fill this in here. Now how do I find the diameter of the sphere?
I just double the radius 1.38 x 2 = 2.76 now we need to find the volume by using the volume formula of a sphere. (4/3Pi radius cubed)
Next, take the radius of 1.38 and plug it in 4/3 times Pi times 1.38 cubed, and I will put this in the calculator. 4/3 x Pi x 1.38 = 11.008 The volume of the sphere will equal 11.008 inches cubed.
You have a backwards sphere problem where you are working from area back to radius, to diameter, and using that information to find the volume of a sphere. The key is you always work from area back to the original linear measure then to a cubed. Thanks for watching and hopefully it helped you find the volume of a sphere.
Common Core Standard G.GMD.3
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Tagged under: geometry ,sphere,radius sphere,volume sphere,diameter sphere,Geometry (Field Of Study),Area (Dimension),Diameter,Radius,Math,Common Core Standard G.GMD.3
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