Surface Area and Volume of a Sphere | MathHelp.com - Free Educational videos for Students in K-12 | Lumos Learning

Surface Area and Volume of a Sphere | MathHelp.com - Free Educational videos for Students in k-12


Surface Area and Volume of a Sphere | MathHelp.com - By MathHelp.com



Transcript
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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