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ivanzaharov [21]
3 years ago
11

He volume of a rectangular prism is 2,058 cubic cm. The length of the prism is 3 times the width. The height is twice the width.

Find the height of the prism.
Mathematics
1 answer:
MrMuchimi3 years ago
3 0

Answer: the height of the prism is 14 cm.

Step-by-step explanation:

The formula for determining the volume of a rectangular prism is expressed as

Volume = length × height × width

Volume = LWH

The length of the prism is 3 times the width. It means that

L = 3W

The height is twice the width. This means that

H = 2W

Therefore,

Volume = 3W × × W × 2W = 6W³

The volume of a rectangular prism is 2,058 cubic cm. This means that

2058 = 6W³

Dividing through by 6, it becomes

343 = W³

W = 7

Therefore, the height of the prism would be

H = 2W = 2 × 7

H = 14 cm

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3 years ago
For his troops' popcorn fundraiser sale, Mike sold caramel corn for $10, buttered microwave popcorn for $8, and lightly buttered
Bad White [126]
\bf \begin{cases}
c=\textit{caramel corn}\\
b=\textit{buttered microwave popcorn}\\
p=\textit{lightly buttered popcorn}
\end{cases}

so... he sold 400 items, that means, whatever those quantities of c,b,p are, they add up to 400, thus

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so, the amount of revenue on the "c" is 10 * c, or 10c
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thus
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he actually sold twice as much, so whatever "b" is, "p" is twice that much
or 
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thus      \bf \begin{cases}
c+b+\boxed{p}=400\\\\
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--------------\\
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\end{cases}

solve for "b", to see how many buttered microwave popcorn Mike sold

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