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sashaice [31]
3 years ago
14

A sphere has a volume of 7,234.56 units^3. Using 3.14 for pi, find the radius of the sphere. Record your answer on the grid.

Mathematics
1 answer:
Ann [662]3 years ago
4 0

Answer:

r = 1728 units

Step-by-step explanation:

Volume of sphere:  V = (4/3)(pi)(r^3), were r is the radius.

Solving this for r^3, we get

      V                           V                          7234.56 units^3

------------- = r^3 = ----------------   so that   --------------------------

(4/3)(pi)                 (4/3)(3.14)                           4.19

Thus, r = 1728 units

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Use rectangle ABCD and the given information to solve each problem.
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Problem 1

<h3>Answers:</h3><h3>angle 6 = 50</h3><h3>angle 7 = 50</h3><h3>angle 8 = 40</h3>

--------------------

Work Shown:

point E = intersection point of diagonals.

x = measure of angle 6

y = measure of angle 8

angle 7 is also x because triangle AED is isosceles (AE = ED)

Focus on triangle AED, the three angles A, E, D add to 180

A+E+D = 180

x+80+x = 180

2x+80 = 180

2x = 180-80

2x = 100

x = 100/2

x = 50

So both angles 6 and 7 are 50 degrees.

Turn to angle 8. This is adjacent to angle 7. The two angles form a 90 degree angle at point A. This is because a rectangle has 4 right angles.

(angle7)+(angle8) = 90

50+y = 90

y = 90-50

y = 40

angle 8 = 40 degrees

=================================================

Problem 2

<h3>Answers:</h3><h3>angle 2 = 61</h3><h3>angle 3 = 61</h3>

--------------------

Work Shown:

Angle 5 is 29 degrees (given). So is angle 4 because these are the base angles of isosceles triangle DEC (segment DE = segment EC)

angle 3 and angle 4 form a 90 degree angle

x = measure of angle 3

(angle 3)+(angle 4) = 90

x+29 = 90

x = 90-29

x = 61

Angle 2 is congruent to angle 3 since triangle BEC is isosceles (BE = EC), so both angle 2 and angle 3 are 61 degrees each.

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4 years ago
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Step-by-step explanation:

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