Question

(a) Can there be a polyhedron with 9 vertices, 9 faces and 16 edges? If yes, then name it.
(b) If a length of 100 m is represented on a map by 1 em, then what will be the actual distance corresponding to 3.75 cm?

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Answer 1

$\large\sf\underline{Question \;no. 1}$

Can there be a polyhedron with 9 vertices, 9 faces and 16 edges? If yes, then name it.

$\large\sf\underline{Answer}$

As per question:

Euler's Formula is for any polyhedrons. i.e.

$\tt\pink{F + V - E = 2}$

$\large\sf\underline{Given}$

• $\sf\:F = 9$

• $\sf\:V = 9$

• $\sf\: E = 16$

According to the formula:

$\sf⟹\:9 + 9 - 16 = 2$

$\sf⟹\:18 - 16 = 2$

$\sf⟹\:2 = 2$

Therefore, these given value satisfy Euler's formula.

$\tt\pink{So\:, \:the \:given\: figure\: is \:a \:polyhedral.}$

For figure refer to the attachment above !

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$\large\sf\underline{Question \;no. 2}$

If a length of 100 m is represented on a map by 1 cm, then what will be the actual distance corresponding to 3.75 cm?

$\large\sf\underline{Given}$

• $\sf\:1cm=100m$

Then, actual distance corresponding to 3.75cm is :

$\sf⟹\:3.75 \times 100$

$\sf⟹\:\frac{375}{100} \times 100$

$\sf⟹\:\frac{37500}{100}$

$\sf⟹\:\frac{375}{1}$

$\tt\pink{➢\:375\:m}$

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• Thnku ❣