Question

1-determine o comprimento e a area de um circulo cujas medidas são:

Answer 1

The question in English
1 Determine the length and area of ​​a circle whose measures are: a) radius 11cm b) radius 4.2 cm c) diameter 42.3 cm

2 considering that a large traditional pizza is 36 cm in radius and a small traditional pizza has 26 cm.Determine the difference between the area of ​​the two pizzas

3.a worker spends 3 hours to clear a circular terrain of 6 meters radius. If the terrain was 12 meters radius, how much time would the worker spend to clean such terrain ???

4, transform the following arcs into radians a) 27 ° b) 81 ° c) 144 ° d) 225 ° d) 315 °

Part 1)
we know that
length of a circle is equal to the circumference
circumference=2*pi*r
area of the circle=pi*r²

part a ) radius 11 cm
circumference=2*pi*11-----> 69.08 cm
area of the circle=pi*11²----> 379.94 cm²

part b) radius 4.2 cm
circumference=2*pi*4.2-----> 26.38 cm
area of the circle=pi*4.2²----> 55.39 cm²

part c ) diameter 42.3 cm
radius r=42.3/2=21.15 cm
circumference=2*pi*21.15-----> 132.82 cm
area of the circle=pi*21.15²----> 1404.59 cm²

Part 2)

area large traditional pizza
r=36 cm
area=pi*36²----> 4069.44 cm²

area small traditional pizza
r=26 cm
area=pi*26²-----> 2122.64 cm²
difference between the area of ​​the two pizzas =4069.44-2122.64
difference between the area of ​​the two pizzas=1946.80 cm²

Part 3)
Area of the circular terrain of 6 meters radius
area=pi*6²-----> 113.04 m²

Area of the circular terrain of 12 meters radius
area=pi*12²-----> 452.16 m²

if a worker spends 3 hours to clear a circular terrain of--------> 113.04 m²
x hours---------------------------> 452.16 m²
x=452.16*3/113.04-----> x=12 hours

Part 4) transform the following arcs into radians
 a) 27°
pi radians------> 180°
x radians-----> 27°
x=27*pi/180-----> x=0.15*pi radians------> 0.47 radians

b) 81°
pi radians------> 180°
x radians-----> 81°
x=81*pi/180-----> x=0.45*pi radians------> 1.41 radians

c) 144°
pi radians------> 180°
x radians-----> 144°
x=144*pi/180-----> x=0.80*pi radians------> 2.51 radians

d) 225°
pi radians------> 180°
x radians-----> 225°
x=225*pi/180-----> x=1.25*pi radians------> 3.93 radians


e) 315°
pi radians------> 180°
x radians-----> 315°
x=315*pi/180-----> x=1.75*pi radians------> 5.50 radians


the answer in Portuguese


Parte 1)

nós sabemos isso
comprimento de um círculo é igual à circunferência
circunferência=2*pi*r
área do círculo=pi*r²

parte a )
raio 11 cm
circunferência=2*pi*11-----> 69.08 cm
área do círculo=pi*11²----> 379.94 cm²

parte b) raio 4.2 cm
circunferência=2*pi*4.2-----> 26.38 cm
área do círculo=pi*4.2²----> 55.39 cm²

parte c )
diâmetro 42.3 cm
raio r=42.3/2=21.15 cm
circunferência=2*pi*21.15-----> 132.82 cm
área do círculo=pi*21.15²----> 1404.59 cm²

Parte 2)


área grande pizza tradicionalr=36 cm
área=pi*36²----> 4069.44 cm²


área pequena pizza tradicional
r=26 cm
área=pi*26²-----> 2122.64 cm²
diferença entre a área das duas pizzas =4069.44-2122.64
diferença entre a área das duas pizzas=1946.80 cm²

Parte 3)

Área do terreno circular de 6 metros de raio
área=pi*6²-----> 113.04 m²


Área do terreno circular de 12 metros de raio
área=pi*12²-----> 452.16 m²

se um trabalhador gastar 3 horas para limpar um terreno -----> 113.04 m²
x hours---------------------------> 452.16 m²
x=452.16*3/113.04-----> x=12 horas

Parte 4) transformar os seguintes arcos em radianos
 a) 27°
pi radianos------> 180°
x radianos-----> 27°
x=27*pi/180-----> x=0.15*pi radianos------> 0.47 radianos

b) 81°
pi radianos------> 180°
x radianos-----> 81°
x=81*pi/180-----> x=0.45*pi radianos------> 1.41 radianos

c) 144°
pi radianos------> 180°
x radianos-----> 144°
x=144*pi/180-----> x=0.80*pi radianos------> 2.51 radianos

d) 225°
pi radianos------> 180°
x radianos-----> 225°
x=225*pi/180-----> x=1.25*pi radianos------> 3.93 radianos


e) 315°
pi radianos------> 180°
x radianos-----> 315°
x=315*pi/180-----> x=1.75*pi radianos------> 5.50 radianos