Question

1) a area lateral de um cilindro equilatero e 25 cm² obtenha a area total e o volume

2) calcule a area lateral do cilindro equilatero 54π cm3 de volume

3) a secçao meridiana de um cilindro equilatero tem 64 cm² de area .Qual e a area lateral do cilindro e do volume

Answer 1

$1)deve~ser~25 \pi cm^{2} \\ A_{lateral}= 2 \pi rh~e~h=2r\Rightarrow A_{lateral}=\large\boxed {4 \pi r^{2} } \\ \\ 4 \pi r^{2} =25 \pi \Rightarrow r^{2}= \dfrac{25}{4} \Rightarrow r= \sqrt{ 6,25 }~ \therefore~r=2,5cm \\ \\ A_{total}=2 A_{base}+ A_{lateral} =2 \pi r^{2} +25 \pi =2 \pi .6,25+25 \pi =37,5 \pi cm^{2} \\ \\ V= \pi r^{2}h= \pi r^{2}.2r= 6,25.2.2,5 \pi~ \therefore ~ \large\boxed {V=31,25 \pi cm^{3} } \\ \\ .$$. \\ \\2) V= \pi r^{2}h= \pi r^{2}.2r=2 \pi r^{3}~~~~~~~~~~~~~~~~~~ A_{lareral}=4 \pi r^{2} \\~~~~ 2 \pi r^{3} =54 \pi~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ A_{lateral} =4 \pi .3^{2} \\~~~~ r^{3}=27 \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\large\boxed { A_{lateral=36 \pi cm^{2} } } \\~~~~ r=\sqrt[3]{27} \\ ~~~~r=3cm \\ \\ .$$. \\ \\3)a~seccao~meridiana~de~um~cilindro~equilatero~e~um~quadrado~cujos~ \\lados ~medem~2r. \\2r.2r=64 \\4 r^{2}=64 \\ r^{2}=16 \\r= \sqrt{16} \\ r= 4cm\\ \\ A_{lateral}= 4 \pi r^{2} ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~V= \pi r^{2}.2r \\ A_{lateral}=4 \pi .16 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~V= \pi.16.2.4 \\ \large\boxed { A_{lateral}=64 \pi cm^{2}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~\larged\boxed {V=128 \pi cm^{3} } \\ \\ .$