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olchik [2.2K]
3 years ago
8

A student said that the surface area of the figure below was 57.4 square centimeters. Is the student correct? Explain.

Mathematics
1 answer:
FrozenT [24]3 years ago
3 0

Answer:

  no

Step-by-step explanation:

The surface area is the sum of the areas of the faces.

There are 4 faces that are 5 cm wide. Their respective heights (from front, over the top) are ...

  1 cm, 2.5 cm, 2 cm, 2.3 cm

for a total height of 7.8 cm. Thus, those 4 faces have a total area of ...

  (5 cm)(7.8 cm) = 39.0 cm^2

__

The two trapezoidal faces each have bases of length 1 and 2 cm, and a "height" of 2.3 cm. Together, their areas are ...

  A = 2×(1/2)(b1 +b2)h = (b1 +b2)h

  A = (1 cm +2 cm)(2.3 cm) = 6.9 cm^2

__

The surface area of the entire trapezoidal prism is then ...

  total area = base area + lateral area = 6.9 cm^2 +39 cm^2

  total area = 45.9 cm^2

The student's answer of 57.4 cm^2 is not correct. (We don't know where that calculation came from.)

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Answer:

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The amount of pennies doubled each day. So the series is,

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As the pennies from each of the previous days are not being stored away until more pennies magically appear so the sum of series will be,

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As we have find the number of days that would elapse before she has a total of more than 90 trillion, so

\Rightarrow 90\times 10^{12}\le \dfrac{1(2^n-1)}{2-1}

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\Rightarrow n \ge \dfrac{\log (90\times 10^{12}+1)}{\log 2}

\Rightarrow n \ge 46.4

\Rightarrow n\approx 47


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