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Dvinal [7]
3 years ago
5

A cube with edges that measure 10 centimeters has a volume that is twice as much as a cube with sides that measure 5 centimeters

. Is this true or false?
Mathematics
1 answer:
rodikova [14]3 years ago
7 0

Answer:

False

Step-by-step explanation:

We find the volumes of the two cubes and compare them.

volume of cube = side^3

The volume of the 10-cm cube is:

V = (10 cm)^3 = 1000 cm^3

The volume of the 5-cm cube is:

V = (5 cm)^3 = 125 cm^3

1000/125 = 8

The volume of the 10-cm cube is 8 times the volume of the 5-cm cube.

The statement is false.

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The length of a rectangle is 6 units and its width is 4 units. What is the approximate length of the diagonal of the rectangle?
ss7ja [257]
The correct answer is:  [D]:  " 7.2 units" .
_______________________________________________________
Explanation:
________________________________________________________
Use the Pythagorean theorem:

a² + b² = c² ;

in which:  "6 units" and "4 units" equal the lengths of the right angle (formed by the rectangle);  and "c" is the length of the diagonal of the rectangle, or the "hypotenuse", of the right triangle formed by the rectangle;  We wish to solve for "c" ;
_______________________________________________

6² + 4² = c² ;  Solve for "c" ;

↔ c² = 6² + 4² ; 

         = (6*6) + (4*4) ;
 
         = 36 + 16 ;

        =  52 ;

    c² = 52 ;

Take the "positive square root" of each side of the equation; to isolate "c" on one side of the equation; and to solve for "c" ; 

  √(c²)  =  √52 ; 

    c = √52 ;  

At this point, we know the 7² = 49 ;  8² = 64 ;  so, the answer is somewhere between "7" and "8" ; yet closer to "7" ;  so among the answer choices given; 

The correct answer is:  [D]:  " 7.2 units" .
_________________________________________
However, let use a calculator:

c = √52 = 7.2111025509279786 ; which rounds to "7.2" ;
   which corresponds to:  
___________________________________________
Answer choice:  [C]:  " 7.2 units" .
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