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3 years ago

Identify the surface area of the composite figure in terms of π.

Mathematics

1 answer:

Katena32 [7]3 years ago

7 0

Answer:

78π m²

Step-by-step explanation:

The lateral area of the cylinder is ...

LA = 2πrh

LA = 2π(3 m)(8 m) = 48π m²

The lateral area of one cone is ...

LA = πrh . . . . where h is the slant height

LA = π(3 m)(5 m) = 15π m²

Then the total surface area of the figure is the area of the two cones plus that of the cylinder:

S = 2(cone area) + cylinder area

S = 2(15π m²) +(48π m²)

S = 78π m²

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Step-by-step explanation:

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$\bf ~~~~~~~~~~~~\textit{function transformations}
\\\\\\
% templates
f(x)= A( Bx+ C)+ D
\\\\
~~~~y= A( Bx+ C)+ D
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f(x)= A(\mathbb{R})^{ Bx+ C}+ D
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--------------------$

$\bf \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\
\bullet \textit{ flips it upside-down if } A\textit{ is negative}\\
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$\bf ~~~~~~\textit{reflection over the y-axis}
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~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by } D\\
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~~~~~~if\ D\textit{ is positive, upwards}\\\\
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with that template in mind, let's check these two

$\bf \stackrel{parent}{y=\cfrac{1}{x}}\qquad \qquad\qquad \qquad \stackrel{transformed}{y=\cfrac{1}{\stackrel{B}{2}x\stackrel{C}{-10}}\stackrel{D}{-3}}\\\\
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B=2\qquad \textit{shrinks horizontally by }\frac{1}{2}
\\\\\\
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Step-by-step explanation:

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