Question

Em um cilindro reto, a área total é 48 pi e a área lateral 30pi, qual o seu volume?

a)30pi
b)34pi
c)40pi
d)45pi
e)50pi

Answer 1

$\large\boxed{\begin{array}{l}\tt dados\begin{cases}\sf A_t=48\pi\\\sf A_l=30\pi\\\sf V=?\end{cases}\\\underline{\boldsymbol{soluc_{\!\!,}\tilde ao\!:}}\\\sf A_t= A_l+2\cdot B\\\sf 48\pi=30\pi+2 B\\\sf 2B=48\pi-30\pi\\\sf 2B=18\pi\\\sf B=\dfrac{18\pi}{2}\\\\\sf B=9\pi\\\sf \backslash\!\!\!\pi \cdot r^2=9\backslash\!\!\!\pi\\\sf r=\sqrt{9}\\\sf r=3\\\sf A_l=2\pi r\cdot h\implies h=\dfrac{A_l}{2\pi r}\\\\\sf h =\dfrac{30\backslash\!\!\!\pi}{2\cdot \backslash\!\!\!\pi\cdot 3}=\dfrac{30}{6}=5\end{array}}}$

$\large\boxed{\begin{array}{l}\underline{\bf C\acute alculo\,do\,volume:}\\\sf V= B\cdot h\\\sf V=9\pi\cdot5\\\sf V=45\pi~u\bullet v\\\huge\boxed{\boxed{\boxed{\boxed{\sf\dagger\red{\maltese}~\blue{alternativa~d}}}}}\end{array}}}$