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Ne4ueva [31]
3 years ago
8

A solid sphere is cut into 4 equal wedges the volume of each wedge is v=1/3r3 solve the volume for r

Mathematics
1 answer:
Dennis_Churaev [7]3 years ago
6 0

Answer:

r = (3V/π)^1/3

Step-by-step explanation:

Given that :

Volume of a sphere = V = 4/3πr³

Dividing into 4

4/3 * 1/4 πr³ = 4/12πr³ = 1/3πr³

V = 1/3πr³

Cross multiply

3V = πr³

Divide both sides by π

3V/ π = πr³/ π

3V/ π = r³

Take the cube root of both sides

r = (3V/π)^1/3

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What is the slant height if the surface area is 395.64 square meters? (Use 3.14 for π .) r = 7 of a cone
kodGreya [7K]
1. The formula for calculate the area of a cone is:

 A=πr²+πrl  (1)

 A is the area (A=395.64 m²).
 π=3.14
 r is the radius (r=7).
 l is the height.

 2. The formula for calculate the slant height of the cone, is given by the Pythagorean theorem:

 h²=l²+r²
 h=√(l²+r²)   (2)

 h is the slant height.

 3. We don't know the value of "l", so:

 - We must rewrite the formula (1) and clear "l":

 A=πr²+πrl 
 A-πr²=πrl
 l=A-πr²/πr

 - Now, we must susbtitute l=A-πr²/πr, into the formula (2). Then, we have:

 h=√(l²+r²) 
 h=√[(A-πr²/πr)²+r²]

 A=395.64 m²
 π=3.14
 r=7

 4. When we substitute the values above into the formula h=√[(A-πr²/πr)²+r²], we obtain the slant height:
 
 h=√[(A-πr²/πr)²+r²]
 h=√170
 h=13 
<span>
 What is the slant height?

 The answer is: D.13</span>
6 0
3 years ago
There are 9 computers and 72 students. What is the unit rate of students to computers?
IRISSAK [1]
The answer is A my dude, this is easy math lol

8 0
3 years ago
Read 2 more answers
What is the surface area of the figure shown? (use 3.14 for pi)
SpyIntel [72]

This is a combination of the formula of several figures.

The first one is the bottom of the cylinder AKA a circle.
The second one is the cylinder - the bottom and the top.
The third one is a cone without a bottom.

The first one can be written like this: r^2*3.14 where r is the radius of the circle
The second one is written like this: 2*3.14*r*h where r is the radius, and h the height
The third one is written like this: l*r*3.14

After this you just have to input the values. 
bottom        cylinder        Cone             (Use calculator if possible)
(3^2*3.14)+(2*3.14*3*5)+(6*3*3.14)=
28.26 + 94.2 + 56.52 = 178.98 in^2

The correct answer is 178.98 in^2.
Youre welcome. 




EXTRA:

If youre wondering how to find the different formulas, you can search for the full formula, then remove the parts you do not need, by matching them with the formula of the part you want to remove.

Example:
Cylinder:
SA = 2(pi<span> r</span><span> 2</span><span>) + (2 </span><span>pi </span><span>r)* h
</span>In this case, i didnt need the top and bottom, then i look for the formula of a circle.
Circle SA = pi r^2

Is this anywhere in the cylinder? Yes! The first part.
Then we are left with:
2 + (2 pi r)*h
But that 2 looks strangely placed, and with some reason, one quickly understands that it means "top AND bottom", but since we removed the circle surface, we have to remove that part too. 
So the final result of the formula is:
2 pi r h


4 0
3 years ago
2^2 times 2^3<br> a.2^4<br> b.2^5<br> c.2^6<br> d.4^6
maxonik [38]

Answer:

The quadratic equations and their solutions are;

9 ± √33 /4 = 2x² - 9x + 6.

4 ± √6 /2 = 2x² - 8x + 5.

9 ± √89 /4 = 2x² - 9x - 1.

4 ± √22 /2 = 2x² - 8x - 3.

Explanation:

Any quadratic equation of the form, ax² + bx + c = 0 can be solved using the formula x = -b ± √b² - 4ac / 2a. Here a, b, and c are the coefficients of the x², x, and the numeric term respectively.

We have to solve all of the five equations to be able to match the equations with their solutions.

2x² - 8x + 5, here a = 2, b = -8, c = 5.                                                  x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(5) / 2(2) = 8 ± √64 - 40/4.     24 can also be written as 4 × 6 and √4 = 2. So                                                                                     x = 8 ± 2√6 / 2×2= 4±√6/2.

2x² - 10x + 3, here a = 2, b = -10, c = 3.                                                   x =-b ± √b² - 4ac / 2a =-(-10) ± √(-10)² - 4(2)(3) / 2(4) = 10 ± √100 + 24/4. 124 can also be written as 4 × 31 and √4 = 2. So                                                                              x = 10 ± 2√31 / 2×2 = 5 ± √31 /2.

2x² - 8x - 3, here a = 2, b = -8, c = -3.                                                    x = -b ± √b² - 4ac / 2a = -(-8) ± √(-8)² - 4(2)(-3) / 2(2) = 8 ± √64 + 24/4.     88 can also be written as 4 × 22 and √4 = 2. So                                                                             x = 8 ± 2√22 / 2×2 = 4± √22/2.

2x² - 9x - 1, here a = 2, b = -9, c = -1.                                                     x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(-1) / 2(2) = 9 ± √81 + 8/4.                                          x = 9 ± √89 / 4.

2x² - 9x + 6, here a = 2, b = -9, c = 6.                                                    x = -b ± √b² - 4ac / 2a = -(-9) ± √(-9)² - 4(2)(6) / 2(2) = 9 ± √81 - 48/4.                                                                             x = 9 ± √33 / 4 .

5 0
2 years ago
Read 2 more answers
The chart shows Jolene's tutoring schedule. Today she worked with both math and
OleMash [197]

Answer:

10

Step-by-step explanation:

5x2=10

4 0
3 years ago
Read 2 more answers
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