Surface Area and Volume of a Sphere | MathHelp.com - By MathHelp.com
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00:0-1 | A Sphere has a volume of 288 pi find its | |
00:05 | area . Leave your answer in terms of pie to | |
00:10 | find the area of the sphere . Remember that the | |
00:13 | formula for the area of a sphere is four pi | |
00:18 | R squared . So in order to find the area | |
00:27 | we first need to find the radius of the sphere | |
00:32 | to find the radius . Let's use are given information | |
00:36 | . Note that we were given that the volume of | |
00:39 | the sphere is 288 pi . And remember that the | |
00:44 | formula for the volume of a sphere is 4/3 pi | |
00:49 | r cubed . So we can set up the equation | |
00:58 | 288 pi equals four thirds pi R cubed . Now | |
01:10 | to solve for R , we first get rid of | |
01:12 | the fraction by multiplying both sides of the equation by | |
01:17 | three what ? On the right side the threes cancel | |
01:28 | . And we're left with four pi r cubed And | |
01:33 | on the left side three times 288 pi is 864 | |
01:40 | pi . So we have 864 pi equals four pi | |
01:47 | r cubed next to isolate the r cubed term . | |
01:53 | We divide both sides of the equation by four pi | |
02:00 | . On the right side the four pies cancel . | |
02:04 | And we're left with R cubed . And on the | |
02:09 | left side the pies cancel . And 864 divided by | |
02:15 | four is 216 . So we have 216 equals r | |
02:22 | cubed . Now since we have an R cubed on | |
02:27 | the right side of the equation to get the are | |
02:30 | by itself , we take the cube root of both | |
02:33 | sides . Yeah on the right side of the cube | |
02:41 | root of R cubed is our . And on the | |
02:46 | left side to find the cube root of 216 we | |
02:51 | make a factor tree . Yeah . 216 is two | |
03:01 | times 108 . 108 is two times 54 , 54 | |
03:11 | Is two times 27 . 27 is three times 9 | |
03:19 | and nine Is three times 3 . Now since we're | |
03:25 | dealing with a cube root , remember that we're looking | |
03:29 | for groups of three factors that are the same . | |
03:32 | And notice that we have 32s And we have three | |
03:38 | threes . Mhm . So a two comes out of | |
03:43 | the radical and three comes out of the radical And | |
03:47 | we have two times 3 or six . So six | |
03:53 | equals r . Which means that the radius of the | |
03:57 | sphere is six . Now that we know the radius | |
04:01 | of the sphere , we can find the area of | |
04:04 | the sphere which is four pi R squared by plugging | |
04:09 | in a six for the are in the formula and | |
04:13 | we have four pi times six squared , which simplifies | |
04:21 | to four pi times 36 Which equals 144 pi . | |
04:31 | So the area of the sphere Is 144 Pi . |
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