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katovenus [111]
2 years ago
11

FIND THE VOLUME OF THE SPHERE

Mathematics
1 answer:
svp [43]2 years ago
4 0

Answer:

about 65.4 inches cubed

Step-by-step explanation:

The formula for the volume of a sphere is 4/3πr^3.

V = 4/3πr^3

   = 4/3π(2.5^3)

   = 20.83π = <u>about 65.4 inches cubed</u>

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Answer:

11 1/4 inches.

Step-by-step explanation:

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The area of trapezoid TRAP is 100 m squared
Anastasy [175]
Answer:  30 m ; (or, write as: "30 meters") .
______________________________________________
Explanation:
____________________

Area of a trapezoid, "A" = (1/2) ( b₁ + b₂) h ;
______________________________________________
or, write as:  A = ( b₁ + b₂) h  / 2 ;
___________________________________
in which:  A = area;
              b₁ = length of "base 1" (choose either one of the 2 (two bases);
              b₂ = length of "base 2" (use the base that is remaining);
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From the information given: 
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A = 100 m² ; 
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b₁ = 10 m
b₂ =  x 
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Find "x", which is:  "b₂" ;
__________________________
      A = ( b₁ + b₂) h  / 2  ;
_____________________________
Plug in our known values; and plug in "x" for "b₂" ; and solve for "x" ;
_________________________________________________________
  100 m² = [(10m + x) (5m)] / 2  ; Solve for "x" ;
_________________________________________________________
          (10m + x) (5m) = (2)* (100m²) ;
_________________________________________________________
             (5m) (10m + x) = 200 m² ;
___________________________________________
Note:  The distributive property of multiplication:
____________________________________________
    a(b+c) = ab + ac ;
 
    a(b−c) = ab <span>− ac ;
</span>____________________________________________

  We have:  (5m) (10m + x) = 200 m²  ;
____________________________________________
So:    (5m) (10m + x) =  (5m*10m) + (5m * x) ;
                           
                               =  50m² + (5m)x  ;
_______________________________________________
     →  50m² + (5m)x = 200m²  ; 
_______________________________________________
Divide the ENTIRE equation by "5m" ;
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     → { 50m² + (5m)x } / 5m = (200m² / 5m) ;
_______________________________________________
     →  10m + x   = 40m ; 
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_______________________________________
     →  10m + x  − 10m  =  40m − 10m ;

to get:

                →    x  =  30 m  ; which is our answer.
___________________________________________________
Answer:  30 m ; (or, write as: "30 meters") .
_____________________________________________________
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