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geniusboy [140]
3 years ago
11

A rectangular prism has a width of 51 ft and a volume of 144 ft3. Find the volume of a similar prism with a width of 17 ft. Roun

d to the nearest tenth, if necessary.
Mathematics
1 answer:
meriva3 years ago
7 0

Answer:

5.3\ ft^3

Step-by-step explanation:

Similar shapes with scale factor k have proportional volumes with coefficient k^3 i.e.

\dfrac{V_{large}}{V_{small}}=k^3,

where

k=\dfrac{\text{width of large prism}}{\text{width of small prism}}.

Since

\text{width of large prism}=51\ ft,\\ \\\text{width of small prism}=17\ ft,

then

k=\dfrac{51}{17}=3.

Hence,

\dfrac{144}{V_{small}}=3^3\Rightarrow V_{small}=\dfrac{144}{27}=\dfrac{16}{3}=5\dfrac{1}{3}\approx 5.3\ ft^3.

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