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kipiarov [429]
3 years ago
13

Tim has a rectangular prism with a length of 10 centimeters, a width of 2 centimeters, and an unknown height. he needs to build

another rectangular prism with a length of 5 centimeters and the same height as the original prism. the volume of the two prisms will be the same. find the width, in centimeters, of the new prism.
Mathematics
1 answer:
ozzi3 years ago
4 0
The volume of the original prism is given by:
 V1 = (10) * (2) * (h)
 rewriting:
 V1 = 20h
 Where,
 h: height
 The volume of the second prism is given by:
 V2 = (5) * (w) * (h)
 We know that the height is the same.
 As the volume is the same then:
 (5) * (w) * (h) = 20h
 Clearing w we have:
 w = (20/5) = 4 cm
 Answer:
 
The width, in centimeters, of the new prism is:
 
w = 4cm
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<u>Given</u><u> </u><u>Information</u><u> </u><u>:</u><u>-</u>

⠀

  • A polygon with 10 sides ( Decagon )

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<u>To</u><u> </u><u>Find</u><u> </u><u>:</u><u>-</u>

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<u>Formula</u><u> </u><u>Used</u><u> </u><u>:</u><u>-</u>

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\qquad \diamond \:  \underline{ \boxed{ \pink{ \sf Exterior ~angle = \dfrac {360^\circ}{no. ~of~sides}}}} \:  \star

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<u>Solution</u><u> </u><u>:</u><u>-</u>

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Putting the given values, we get,

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\sf \dashrightarrow Exterior ~angle =  \dfrac{360  ^\circ}{10} \:  \:   \\  \\  \\ \sf \dashrightarrow Exterior ~angle =  \frac{36 \cancel{0}^\circ}{ \cancel{10}} \:  \:   \\  \\  \\ \sf \dashrightarrow Exterior ~angle =  \underline{ \boxed{ \frak{ \red{36^\circ}}}} \: \star \\  \\

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\underline{ \rule{227pt}{2pt}} \\  \\

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