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3 years ago

Find the lateral area of the regular prism with height h, if the base of the prism is:

Mathematics

1 answer:

rjkz [21]3 years ago

6 0

Answer:

The lateral area of the prism is $84\ cm^{2}$

Step-by-step explanation:

we know that

The lateral area of the regular prism is equal to

$LA=Ph$

where

P is the perimeter of the base of the prism

h is the height of the prism

Find the perimeter of the base

$P=6(3.5)=21\ cm$ ----> is a regular hexagon (6 equal sides)

we have

$h=4\ cm$

substitute

$LA=(21)(4)=84\ cm^{2}$

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Answer:

Therefore surface integral is $\pi(a^2+b^2)c-0-0=\pi(a^2+b^2)c$ .

Step-by-step explanation:

Given function is,

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To find,

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$\int\int_{S}\vec{F}dS$

$=\int\int\int_V\nabla.\vec{F}dV$

$=\int\int\int_V(\frac{b}{a}+\frac{a}{b})dV$

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$=\frac{a^2+b^2}{ab}\times \textit{Volume of the elliptic cylinder}$

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If unit vector $\cap{n}$ directed in positive (outward) direction then z=c and,

$\int\int_{S_1}\vex{F}.dS_1=\int\int_{S_1} . dA$

$=\int\int_{S_1}.dA=0$

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$\int\int_{S_2}\vex{F}.dS_2=\int\int_{S_2}. -dA$

$=\int\int_{S_2}. -dA=0$

Therefore surface integral without unit vector of the surface is,

$\pi(a^2+b^2)c-0-0=\pi(a^2+b^2)c$

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