Question

1. Find the circumference of the circles, given that:
(a) radius = 21 mm
(b) diameter = 14 cm
2. Find the area of the circles, given that: (a) radius = 20 cm (b) diameter = 42
3. Find the radius of a circle whose circumference is 39.6 cm.
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Answer 1

Resposta:

1) ( a ) 131,88 mm

1) ( b ) 43,96 cm

2) ( a ) 125,6 cm

2) ( b ) 131,88 cm

3) 6,3 cm ( approximate value )

Explicação passo-a-passo:

Text of the Questions:

1. Find the circumference of the circles, given that:

(a) radius = 21 mm

(b) diameter = 14 cm

2. Find the area of the circles, given that: (a) radius = 20 cm (b) diameter = 42

3. Find the radius of a circle whose circumference is 39.6 cm.

Answers:

1. Find the circumference of the circles, given that:

(a) radius = 21 mm

(b) diameter = 14 cm

Note 1 → In almost all questions, basically you want to find out what is the circumference, given the value of the radius.

So you want to know the measure of the perimiter of  each circumferences.

Note 2 → There is a formula that gives the circumference when you know the radius:

radius = circumference / 2π

( with 3,14 for pi (π) , in my calculations )

Which can be transformed into    " radius * 2π = circumference "

1 ) (a) radius = 21 mm  ⇒  21 * 2 * 3,14 = 131,88 mm

1 ) (b)  

diameter = 14 cm

Since diameter = 2 * radius

The radius here is 14/2 = 7 cm

Using the same formula:

radius = 7 cm  ⇒  7 * 2 * 3,14 = 43,96 cm

 

2) (a)  radius = 20 cm

Again the same formula:

radius = 20 cm  ⇒  20 * 2 * 3,14 =  125,6 cm

2) (b) diameter = 42 cm

Radius = diameter/ 2

Radius = 42 / 2 = 21 cm

The same value as 1) ( a)  131,88 cm , only changing the unit of measure

3) Circumference  = 39,6 cm  

Always using the same formula:

radius * 2π = circumference

radius = ( circumference) / ( 2π )

radius = 39,6/ ( 2 * 3,14 )

 

Radius ≈ 6,3 cm ( approximate value )

Study well

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Operative signs :  ( * )  multiplication      ( / )  division    

( ≈ ) approximate value    ( ⇒ ) implies that