Calcule a área e o volume dos cilindros a) 8cm r=3 cm b) 4cm 1...

1.-) Resposta
r = 4 m ; h = 6 m ; Al = ???

Area lateral >

Al = 2 x pi x r x h
Al = 2 x pi x 4 x 6
Al = 2 x pi x 24
Al = pi x24 x 2
Al = pi x 48
Al = 3,14 x 48
Al =150,72 m^2

2.-) Resposta :
r = 5cm ; h = 3x-->h = 3 x 5--> h = 15cm
At =???

At = 2(pi x r^2) + 2(pi x r x h)
At = 2(pi x (5)^2) + 2(pi x 5 x 15)
At = 2(pi x 25) +2(pi x 5)
At = 2(3,14 x 25) + 2(3,14 x 75)
At = 2(78,50) + 2(235,50)
At = 157 + 471
At = 628 cm^2

3.-) Resposta :
h = 36 cm ; r = 36 x 1/3-->r = 36/3 -->r = 12 ; V=???

Volume >

V = pi x r^2 x h
V = pi x (12)^2 x 36
V = pi x 144 x 36
V = pi x5.184
V = 3,14 x 5.184
V = 16.277,76 cm^3

4.-) Resposta :
diametro e 20cm
r = D/2-->r =20/2-->r=10

Area da base >

Ab = pi x r^2
Ab = pi x(10)^2
Ab = pi x 100
Ab = 3,14 x 100
Ab = 314 cm^2

5.-)Resposta :
ciclindro circular reto
r =3cm ; h =3cm ;V= ???

Volume >

V = 2 x pi x r x h
V = 2 x pi x 3 x 3
V = 2 x pi x 9
V = pi x 2 x 9
V = pi x 18
V = 3,14 x 18
V = 56,52cm^3

6.-)Resposta :
D =24 cm ---> r = D /2 ---> r = 24/2---> r = [email protected]
h = 38m
At = ???

At = 2(pi x r^2 ) + 2(pi x r x h)
At = 2 (pi x (3)^2) +2 (pi x 3 x 3)
At = 2(pi x 9) + 2(pi x 9)
At = 2(3,14 x 9) + 2(3,14 x 9)
At =2(228,26) + 2(28,36)

At = 456,72 + 456,72
At = 913,44cm^2

7.-) Reposta :
D = 12cm-->r = D/2--->
r = 12/2 --->r = 6cm
h = 5cm

At = 2 (pi x r) + 2(pi x r x h)
At = 2 (pi x 6) + 2(pi x 6 x 5 )
At = 2 (3,14x6) + 2( 3,14 x30)
At = 2(18,84) + 2 (94,20)
At = 37,68 + 47,10
At = 84,78 cm^2

8.-)Resposta :
D = 10cm--->r=D/2
-->r=10/2--> r = 5 cm
h = 12cm

Volume >

V = 2 x pi x r x h
V = 2 x pi x 5 x 12
V = 2 x pi x 60
V = pi x 2 x 60
V = pi x 120
V = 3,14 x 120
V = 376,80 cm^3

9.-) resposta:
Al = 250 pi cm^2
r = 40cm
h = ???

Al = 2 x pi x r x h

250 pi cm^2 = 2 x pi x 40 x h
excluimos pi fica assim
250 = 2 x 40 x h
250 = 80 x h
80xh = 250
h = 250 / 80
h = 3,125 cm

10.-) Resposta :
Area da base = Area lateral
h = 12cm

Area da base (formula)
Ab =pi x r^2

Area lateral (formula)
Al = 2 x pi x r x h

¤vamos igualar Ab = Al

Ab = Al
pi x r^2 = 2 x pi x r x h
3,14 xr^2 = 2x3,14xrx12
3,14xr^2 = 6,28 x r x 12
3,14xr^2 = 6,28 x 12 x r
3,14xr^2 = 75,36x r
vamos igualar a zero
3,14 x r^2 - 75,36 x r = 0
vamos fatorizar
3,14.r (r - 24) = 0
+3,14.r = 0 --> r = 0/3,14--> r = 0 descartado
+r - 24 = 0--> r = 24
entao o raio e r = 24cm

¤ Volume

V = pi x r^2 x h
V = pi x (24)^2 x 12
V = pi x 576 x 12
V = pi x 6.912
V = 3,14 x 6.912
V = 21.703,68cm^3

11.-) resposta:
r =150m; Al =900pi m^2
h=???

Al = 2 x pi x r x h
900pi = 2xpix150xh
900pi =150 x 2 x pi x h
900pi = 300 x pi x h
vamos excluir pi fica assim
900 = 300xh
300xh = 900
h = 900/300
h = 3m

12.-) Resposta :
r =10cm ; Ab = Al
h = ???

vamos igualar a Ab = Al
Ab = Al
pi x r^2 = 2 x pi x r x h
pi x (10)^2 = 2xpix10xh
pi x 100 = 2x10xpixh
pi x 100= 20pi x h
vamos excluir pi ficam assim
100 = 20xh
20xh = 100
h = 100/20
h = 5cm

13.-) Resposta :
V = 54picm^3 , h = 2r

¤Volume >

V = pi x r^2 x h
54pi = pi x r^2 x 2r
54pi = pi x r^3 x 2
vamos excluor pi ficam assim
54 = r^3 x 2
2.r^3 = 54
r^3 = 54/2
r^3 = 27
r = 3/27
(porque3x3=9x3= 27 entao 3 vezes 3 da 27)
r = 3cm

¤ Area total (At)

At = 2x r x 2 x r + 2 x r^2 x pi
At = 2 x 3 x 2 x 3 + 2 x (3)^2 x pi
At = 6x6 +2 x 9 x pi
At = 36 + 18 x pi
At = 36 + 18 (3,14)
At = 36 + 56,52
At = 92,52 cm

14.-) Resposta :
Ab = 12,56cm^2
Al =???
r = ???

¤vamos a calcular a area lateral que temos :
tambem lembre que a area lateral e o dobro.

Al = 2 x Ab
Al = 2 x 12,56
Al = 25.12cm^2

¤ vamos encontrar o raip com a formula da area da base :

Ab = pi x r^2
12,56 = 3,14 x r^2
3,14xr^2 = 12,56
r^2 = 12,56/3,14
r^2 = 4
r = / 4
r = 2cm

¤ vamos calcular a altura com a formula da area latreal na siguente maneira :

Al = 2 x pi x r x h
25,12 = 2 x 3,14 x 2 x h
25,12 = 6,28 x 2 x h
25,12 = 12,56 xh
12,56xh = 25,12
h =25,12/12,56
h = 2cm

15.-) Resposta :
h = 6/6 cm
V = 36/6picm^3

¤vamos usar a formula de volume

V = Ab x h
36/6.pi = Ab x 6/6
6/6 .Ab = 36/6
Ab = 36/6.pi

6/6

Ab = 6.pi cm

¤vamos calcular a area da base para encontrar o raio

Ab = pi x r^2
6.pi = pi x r^2
vamos excluir pi ficam assim
6 = r^2
r^2 = 6
r = /6 cm

¤vamos calcular a area
lateral

Al = 2 x pi x r x h
Al = 2 x pi x / 6 x 6/ 6
Al = 2 x pi x 6/36
Al = 2 x pi x 6 x 6
Al = 2x pi x 36
Al = 2 x 36 x pi
Al = 72 x pi cm^2

¤vamos calcular a area total na siguente maneira

At = 2 x Ab + Al
At = 2 x 6.pi +72.pi
At = 12.pi + 72.pi
At = 84.pi cm^2​