Question

o volume do cone é 12 pi metros cúbicos e o raio da base é 3 metros, determine as áreas da base, lateral e total.

Answer 1

12π =  . π . 3² . h
12π =  . π . 9 . h
12π = 3π . h
4π = h

g² = R² + h²
g² = 3² + 4π²
g² = 9 + 16π
g² = 25π
g = √25π
g = 5π

Ab = π . 3²
Ab = 9π

Al = π . 3 . 5π
Al =  3π . 5π
Al = 15π

At = Al + Ab
At = 15π + 9π
At = 24π

Answer 2

V = 1/3 ( π r² h )
 
 12π = 1/3 (π 3² h)
 
12π = 1/3 (9πh)

12π = 3πh

h = 12π/3π    h = 4 m

Sb = π r²       Sb = π 3²    Sb = 9π m²

Sl = π r g

g² = 3² + 4²       g² = 9 + 16     g² = 25      g =√25      g = 5 m 

Sl = π . 3 . 5   Sl = 15π m²

St = Sb + Sl          St = 15π + 9π =  24π m²  resposta