Question

Uma esfera possui 36 pi cm³ de volume, qual e a area dessa esfera?obs: calcule em primeiro lugar o raio da esfera e depois a area.

Answer 1

Olá


Volume = 36π³



Encontrando o raio.


$\displaystyle\mathsf{V= \frac{4}{3}\pi r^3 }\\\\\\\mathsf{36\pi= \frac{4}{3}\pi r^3}\\\\\\\mathsf{ \frac{3}{4}36\pi = \pi r^3}\\\\\\\mathsf{ \frac{27\pi}{\pi}=r^3 }\\\\\\\mathsf{r= \sqrt[3]{27} }\\\\\\\boxed{\mathsf{r=3~cm}}$



Calculando a Área

$\displaystyle \mathsf{A=4\pi r^2}\\\\\\\mathsf{A=4\pi\cdot (3)^2}\\\\\\\boxed{\mathsf{A=36\pi~m^2}}$