Question

36 Nos cálculos, use = 3.1.

a)Qual destas regiões planas tem maior medida de perímetro a circular ou a retangular? E qual tem maior medida de área?

b)Qual destes sólidos geométricos tem maior me dida de volume o cubo o bloco retangular ou o lindo? E a menor medida de volume?​

Answer 1

a)

Área do círculo:

$\boxed{\boxed{A = \pi\cdot\!\,r^2}}\bigstar\\\\A= 3,1\cdot5^2\\\\A=3,1\cdot25\\\\\boxed{A=77,5~cm^2}\checkmark~\hookleftarrow~\largeMaior~\acute{A}rea$

Perímetro do círculo:

$\boxed{\boxed{P=2\pi\!\,r}}\bigstar\\\\P=2\cdot3,1\cdot5\\\\ P= 10\cdot3,1\\\\\boxed{P=31~cm}\checkmark$

Área do retângulo:

$\boxed{\boxed{A=b~\cdot~h~\Rightarrow~A=C~\cdot~L}}\bigstar\\\\A= 12\cdot5\\\\\boxed{A=60~cm^2}\checkmark$

Perímetro do retângulo:

$\boxed{\boxed{P=2\!\,b+2\!\,h}}\bigstar\\\\P=2\cdot12+2\cdot5\\\\P=24+10\\\\\boxed{P=34~cm}\checkmark~\hookleftarrow~\largeMaior~Per\acute{\imath}metro$

b)

Volume do cubo:

$\boxed{\boxed{V=A_{(base)}\cdot~h~\Rightarrow~V=a\cdot~a\cdot~a~\Rightarrow~V=a^3}}\bigstar\\\\V=a^3\\\\V=4^3\\\\\boxed{V=64~cm^3}\checkmark~\hookleftarrow~\largeMaior~Volume$

Volume do bloco retangular:

$\boxed{\boxed{V_{(B)}=abc}}\bigstar\\\\V_{(B)}=4\cdot3\cdot5\\\\\boxed{V_{(B)}=60~cm^3}\checkmark$

Volume do cilindro com diâmetro:

$\boxed{\boxed{V=\pi\cdot\left(\frac{d}{2}\right)^2\cdot~h}}\bigstar\\\\V=3,1\cdot\left(\frac{\diagup\!\!\!\!4}{\diagup\!\!\!\!2}\right)^{2}\cdot5\\\\V=3,1\cdot2^2\cdot5\\\\V=3,1\cdot4\cdot5\\\\\boxed{V=62~cm^3}\checkmark$