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3 years ago

10

Bernard is training for a race . He performs the same exercise routine every day. In a 7 day week does Bernard spend more time w

eight lifting or jogging?howmuch more time?

1 answer:

prisoha [69]3 years ago

8 0

The hidden question is how much time does Bernard spend weight lifting in 1 week because the answer to jogging is already there, which is 140

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A hemisphere has an area of 256 pi cm^2. What is its volume?

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$\bf \begin{array}{llll}
\textit{surface area of a sphere}\\\\
A=4\pi r^2
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\textit{a hemisphere is half that}\\\\
A=\cfrac{4\pi r^2}{2}\implies A=2\pi r^2
\end{array}\qquad r=radius
\\\\\\
\textit{now, we know the area is }256\pi \implies 256\pi =2\pi r^2
\\\\\\
\cfrac{256\pi }{2\pi }=r^2\implies \sqrt{128}=r\implies \boxed{8\sqrt{2}=r}
\\\\
-----------------------------\\\\$

$\bf \textit{volume of a sphere}\\\\
V=\cfrac{4}{3}\pi r^3\qquad r=radius
\\\\\\
\textit{a hemisphere is half that}\\\\
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\\\\\\
V=\cfrac{2\pi r^3}{3}
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\textit{now, we know the radius is }8\sqrt{2}\implies V=\cfrac{2\pi (8\sqrt{2})^3}{3}
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V=\cfrac{2\pi (8^3\sqrt{2^3})}{3}\implies V=\cfrac{2\pi \cdot 512\cdot 2\sqrt{2}}{3}
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\boxed{V=\cfrac{2048\pi \sqrt{2}}{3}}$

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