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uranmaximum [27]
3 years ago
10

Cube A is inscribed in sphere B, which is inscribed in cube C. If the sides of cube A have length 4, what is the volume of cube

C?
Mathematics
1 answer:
Aleks04 [339]3 years ago
4 0

Answer:

The volume of cube C is

V=192\sqrt{3}\ units^3

Step-by-step explanation:

step 1

Find the diameter of sphere B

we know that

When a cube is inscribed in a sphere, the long diagonal of the cube is a diameter of the sphere

Let

L ----> the length side of cube A

d ----> the diagonal of the base of cube A

D ---> the long diagonal of cube A

Find the diagonal of the base of cube A

Applying the Pythagorean Theorem

d^2=L^2+L^2

we have

L=4\ units

substitute

d^2=4^2+4^2\\d^2=32\\d=4\sqrt{2}\ units

Find the long diagonal of cube A

Applying the Pythagorean Theorem

D^2=d^2+L^2

substitute

D^2=32+4^2\\D^2=48\\D=4\sqrt{3}\ units

step 2

we know that

If sphere B is inscribed in cube C, then the length side of cube C is equal to the diameter of sphere B

Let

c ----> the length side of cube C

we have that

c=4\sqrt{3}\ units

The volume of cube C is equal to

V=c^3

substitute

V=(4\sqrt{3})^3

V=192\sqrt{3}\ units^3

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DochEvi [55]
The answer is B.

I hope this helps!
7 0
3 years ago
6x+7y=4x+4y6x+7y=4x+4y6, x, plus, 7, y, equals, 4, x, plus, 4, y Complete the missing value in the solution to the equation. (((
Dmitrij [34]

Answer:

<h3>The missing value in the given solution is x=6</h3><h3>Therefore the solution is (6,-4)</h3>

Step-by-step explanation:

Given equation is 6x+7y=4x+4y\hfill (1)

<h3>To find the missing value in the solution to the equation :</h3>
  • Let missing value in the solution be x
  • Then the solution of the given equation is (x,-4)

Substitute the value of y=-4 in the given equation (1) we get

6x+7(-4)=4x+4(-4)

6x-28=4x-16

6x-28-(4x-16)=4x-16-(4x-16)

6x-28-4x+16=4x-16-4x+16 ( adding the like terms )

2x-12=0

2x=12

x=\frac{12}{2}

Therefore x=6

<h3>Therefore the missing value in the given solution is x=6</h3><h3>Therefore the solution is (6,-4)</h3>

8 0
3 years ago
Question 3- Please help. Find the area of the sector for the image below:
bezimeni [28]

Answer:

The answer is 16.8 cm^ 2.

6 0
3 years ago
Solve the equation for x in simplest form
spayn [35]

Answer:

A x=1/4

Step-by-step explanation:

2/3x = 1/6

Divide by 2/3

so 1/6 ÷ 2/3

= 1/6 • 3/2

= 3/12

= 1/4

4 0
3 years ago
Maya had $27. She spent all the money on buying 3 burgers for $x each and 2 sandwiches for $y each. If Maya would have bought 2
defon

Answer:

Option C

The student's conclusion is correct because the solution to the system of equations 3x+2y=27  and 2x+y=16 is (5,6)

Step-by-step explanation:

Let

x------> the cost of each burger

y-----> the cost of each sandwich

we know that

3x+2y=27 -----> equation A

2x+y=(27-11)

2x+y=16 ----> equation B

Solve the system of equations

Multiply the equation B by -2

-2(2x+y)=-2*16 ----->-4x-2y=-32 ------> equation C

Adds equation A and equation C

3x+2y=27 \\-4x-2y=-32\\ ----------\\ 3x-4x=27-32\\ -x=-5\\x=5

Substitute the value of x in the equation B

2(5)+y=16

10+y=16

y=6

The solution of the system of equations is the point (5,6)

so

The price of each burger is \$5

The price of each sandwich is \$6

6 0
2 years ago
Read 2 more answers
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