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slava [35]
3 years ago
14

If the volume of a sphere inscribed in a cubic box is 36pi, find the surface area of the box

Mathematics
1 answer:
Kruka [31]3 years ago
3 0

Answer:

Surface area of the cube = 216 square units

Step-by-step explanation:

Let the length of a side of a cube = x unit

Diameter of the sphere inscribed in this cube = length of a side of the cube

Volume of the sphere = \frac{4}{3}\pi r^{3}

Where r = radius of the sphere = \frac{x}{2} units

36π = \frac{4}{3}\pi (\frac{x}{2})^{3}

36π = \frac{4x^{3}\pi }{24}

36×24 = 4x³

x = \sqrt[3]{\frac{36\times 24}{4} }

x = 6 units

Length of a side of the cube = 6 units

Surface area of the cube = 6×(Side)²

                                          = 6×(6)²

                                          = 216

                                          = 216 square units    

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Which expression has a value of 1/36?
Schach [20]
(1/36) = 0.0277777777778

(1/108)^3 = 7.9383224102<span> x 10^-7 </span>
(1/9)^4 = 0.000152415790276
(1/6)^2 = 0.0277777777778
(1/2)^5 =  <span>0.03125

The only one that matches with the value of 1/36 is (1/6)^2. Therefore, your answer is C. (1/6)^2
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6 0
3 years ago
Read 2 more answers
2. Explain how the order of operations determines how you simplify a numeric expression. Be sure to explain the rules for additi
IgorLugansk [536]
P-paratheses (do any math that has parentheses around the numbers) y=(2x5)+25
E-exponents (do the exponents next) y=(2x5)+5^2
M-multiplying. (Basically everything is self explanatory from here to then cuz im lazy to list examples)
Just basically if you don't use PEMDAS, you'll get the wrong answer
4 0
3 years ago
Whats the correct answer ?
11Alexandr11 [23.1K]

Answer:

$80, $48

Step-by-step explanation:

The original price was x.

The price is reduced by 40%. The markdown is 40% of x, or 0.4x.

The actual dollar amount of the markdown is $32.

That means that 0.4x must equal $32.

We set up an equation and solve for x, the original price.

0.4x = 32

Divide both sides by 0.4

x = 32/0.4

x = 80

The original price is $80.

The markdown is $32.

$80 - $32 = $48

The marked down price is $48.

Answer: $80, $48

3 0
3 years ago
A collection of nickels and dimes is worth $6.10. There are 67 coins in all. how many nickels are there?
Dmitrij [34]

 Question 1:

 For this case, the first thing we must do is define variables.
 We have then:
 x: number of nickels
 y: number of dimes
 We write the system of equations that adapts to the problem.
 We have then:
 0.05x + 0.10y = 6.10
 x + y = 67
 Solving the system we have:
 x = 12
 y = 55
 Answer:
 there are 12 nickels

 Question 2:

 For this case, the first thing we must do is define variables.
 We have then:
 x: Allan's score
 y: Dave's score
 We write the system of equations that adapts to the problem.
 We have then:
 x + y = 375
 x = 2y-60
 Solving the system we have:
 x = 230
 y = 145
 Answer:
 
Dave: 145 Allan: 230
7 0
3 years ago
Pls can someone pls help me <br> Please show your work
Lana71 [14]

Answer:

x = 8

I dunno what the question is in the first place, but I assume you are solving for x.

Step-by-step explanation:

The two given angles are equivalent because they are parallel and they have a line that intersects.

The line creates two angles on each side of each line, which is 120 or 60 because there are 180 degs on a straight line.

The obtuse side is 120, and the -8 + 16x is also on an obtuse angle, showing that they are equal.

120 = -8 + 16x

128 = 16x

8 = x

x = 8

7 0
2 years ago
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