Question

Qual é o volume de um cilindro circular reto, cuja base está inscrita num quadrado de 40 cm de perímetro e cujo raio da base é a metade da altura?
a) 72 π cm³
b) 125 π cm³
c) 250 π cm³
d) 272 π cm³
e) 276 π cm³

Answer 1

$\Large\boxed{\begin{array}{l}\sf o\,di\hat ametro\,da\,circunfer\hat encia\\\sf \acute e\,igual\,ao\,lado\,do\,quadrado.\\\sf p_{quadrado}=4\cdot \ell \\\sf 40=4\cdot\ell\\\sf \ell=\dfrac{40}{4}\\\sf\ell=10\,cm\\\sf d=\ell\\\sf 2r=10\\\sf r=\dfrac{10}{2}\\\sf r=5\,cm\\\sf se\,o\,raio\,da\,base,\acute e\,igual\\\sf a\,metade\,da\,altura,ent\tilde ao\\\sf a\,altura\,vale\,o\,dobro\,do\,raio.\\\sf h=2\cdot r\\\sf h=10\,cm\end{array}}$

$\Large\boxed{\begin{array}{l}\underline{\rm C\acute alculo\,da\,\acute area\,da\,base}\\\sf B=\pi\cdot r^2\\\sf B=\pi\cdot 5^2\\\sf B=25\pi\,cm^2\\\underline{\rm C\acute alculo\,do\,volume\,do\,cilindro}\\\sf V=B\cdot h\\\sf V=25\pi\cdot 10\\\sf V=250\pi\,cm^3\\\huge\boxed{\boxed{\boxed{\boxed{\sf\red{\maltese}~\blue{alternativa~c}}}}}\end{array}}$