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Nady [450]
3 years ago
6

What is the approximate volume of the pyramid?

Mathematics
2 answers:
adelina 88 [10]3 years ago
5 0
Just multiply all of the numbers and you will get 1472 ft3
Margaret [11]3 years ago
3 0
The correct answer is:  [C]:  " 491 ft³ " .
_______________________________________________
Explanation:
_______________________________________________
Note the formula/equation for the volume of a pyramid: 

Volume of a pyramid, "V" :  

V  =  (⅓) *(base area) *
    (perpendicular height; that is height measured from center of base to                                                                                                                apex) ; 
_______________________________________________________
  base area (which is a square, in this case)  =
                            length * width  =   8 ft * 8 ft  =  64 ft ² ; 
_______________________________________________________
  perpendicular height  =  23 ft ;
_______________________________________________________

V = (⅓) * (64 ft ²) * (23 ft) ; 

=  [(64 ft ²) *(23 ft)] / 3 = 1472 ft³ / 3 ;

= 490. 66666...  ft³ ; (that is; "490 ⅔  ft³ ") ;  which is closest to (rounds up to):

Answer choice:  [C]:  491 ft³  .
_______________________________________________
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Answer:

<h3>B = 48.7° , C = 61.3° , b = 12</h3>

Step-by-step explanation:

In order to find B we must first angle C

To find angle C we use the sine rule

That's

\frac{ |a|  }{ \sin(A) }  =  \frac{ |c| }{ \sin(C) }

From the question

a = 15

A = 70°

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So we have

\frac{15}{ \sin(70) }  =  \frac{14}{ \sin(C) }

\sin(C)  =  \frac{14 \sin(7 0 ) }{15}

C = \sin^{ - 1} (  \frac{14 \sin(70) }{15} )

C = 61.288

<h3>C = 61.3° to the nearest tenth</h3>

Since we've found C we can use it to find B.

Angles in a triangle add up to 180°

To find B add A and C and subtract it from 180°

That's

A + B + C = 180

B = 180 - A - C

B = 180 - 70 - 61.3

<h3>B = 48.7° to the nearest tenth</h3>

To find b we can use the sine rule

That's

\frac{ |a| }{ \sin(A) }  =  \frac{ |a| }{ \sin(B) }

\frac{15}{ \sin(70) }  =  \frac{ |b| }{ \sin(48.7) }

|b|  =  \frac{15 \sin(48.7) }{ \sin(70) }

b = 11.9921

<h3>b = 12.0 to the nearest tenth</h3>

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