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meriva
3 years ago
7

What is the surface area of a sphere if its volume is 288π cubic inches? Leave your answers in terms of π. A. 216π in² B. 144π i

n² C. 288π in² D. 16π in²
Mathematics
1 answer:
Keith_Richards [23]3 years ago
4 0

Remark

The Volume of a sphere is V = (4/3) pi r^3. From that, you need to find r.

Givens

V = 288*pi

Substitute

288 pi = (4/3) pi r^3 Divide both sides by pi

288 pi/pi = (4/3) pi r^3 / pi

288 = (4/3) r^3 Multiply by 3

288*3 = 4*r^3

864 = 4r^3 Divide by 4

864 / 4 = 4 r^3 / 4

216 = r^3

Take the cube root of both sides.

cube_root(r^3) = cube_root(216)

r = 6

Surface Area

Formula

Area = 4 pi r^2

Substitute

r = 6

Area = 4 * pi * 6^2

Area = 4*36 * pi

Area = 144 pi Answer

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How many times larger is 2 x 1012 than 5 x 106?
vfiekz [6]

Answer: It is 3.81886792453 times larger

Step-by-step explanation: 2 x 1012 is 2024

5 x 106 is 530

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6 0
3 years ago
Are these parallelograms congruent?<br> 4 cm<br> 6 cm<br> 6 cm<br> 9 cm<br> yes<br> no
lianna [129]

Answer:

Step-by-step explanation:

Yes 6 over 9 simplifys to 2 over 3.

And 4 over 6 simplifys down to 2 over 3

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7 0
3 years ago
M is between points C and Q. CM=17 and CQ=21. What is MQ?
katrin2010 [14]
Sometimes it helps to draw it out...

     (17)
C_______M_________Q
|___________________|
             21

therefore, CM + MQ = CQ
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8 0
3 years ago
Read 2 more answers
What are the solutions to the equation 2(x-3)^2=54 ?
erastova [34]

Answer:

      x =(6-√108)/2=3-3√ 3 = -2.196

 x =(6+√108)/2=3+3√ 3 = 8.196

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

2 • (x - 3)2 - 54 = 0

Step  2  :

 2.1    Evaluate :  (x-3)2   =  x2-6x+9 

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   2x2 - 12x - 36  =   2 • (x2 - 6x - 18) 

Adding  9  has completed the left hand side into a perfect square :

   x2-6x+9  =

   (x-3) • (x-3)  =

  (x-3)2  (x-3)1 =

   x-3

Now, applying the Square Root Principle to  Eq. #4.3.1  we get:

   x-3 = √ 27

Add  3  to both sides to obtain:

   x = 3 + √ 27

Since a square root has two values, one positive and the other negative

   x2 - 6x - 18 = 0

   has two solutions:

  x = 3 + √ 27

   or

  x = 3 - √ 27

Solve Quadratic Equation using the Quadratic Formula

 4.4     Solving    x2-6x-18 = 0 by the Quadratic Formula .

 According to the Quadratic Formula,  x  , the solution for   Ax2+Bx+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

                                     

            - B  ±  √ B2-4AC

  x =   ————————

                      2A

  In our case,  A   =     1

                      B   =    -6

                      C   =  -18

Accordingly,  B2  -  4AC   =

                     36 - (-72) =

                     108

Applying the quadratic formula :

               6 ± √ 108

   x  =    —————

                    2

Can  √ 108 be simplified ?

Yes!   The prime factorization of  108   is

   2•2•3•3•3 

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a square i.e. second root).

√ 108   =  √ 2•2•3•3•3   =2•3•√ 3   =

                ±  6 • √ 3

  √ 3   , rounded to 4 decimal digits, is   1.7321

 So now we are looking at:

           x  =  ( 6 ± 6 •  1.732 ) / 2

Two real solutions:

 x =(6+√108)/2=3+3√ 3 = 8.196

or:

 x =(6-√108)/2=3-3√ 3 = -2.196

7 0
3 years ago
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