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const2013 [10]
3 years ago
6

Describes two different rectangles prisms you could make from16 unit cubes

Mathematics
1 answer:
quester [9]3 years ago
5 0
The volume of the prism=volume of cube
l*b*h=16(1*1*1) , since it is a unit cube
l*b*h= 16, number of possibilities for 16 are 16*1*1,2*8*1,4*4*1,2*2*4.
Please do not take fractions into consideration because it is a unit cube only integer values will be accepted for l,b and h.
So, total 4 possibilities.
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Answer:

The most correct option is;

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Step-by-step explanation:

From the question, the dimension of each square = 3 ft.²

Therefore, the length of the sides of the square = √3 ft.

Based on the above dimensions, the dimension of the small semicircle is found by counting the number of square sides ti subtends as follows;

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∴ The dimension of the diameter of the large semicircle = 22·√3

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Area of the large semicircle = (π·r²)/2 = (π×(11·√3)²)/2 = 570.2 ft.²

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A_{(segment \, of \, semicircle)} = \frac{1}{4} \times (\theta - sin\theta) \times r^2

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\theta = 2\times tan^{-1}( \frac{The \, number \, of  \, vertical  \, squrare  \, sides  \ cut  \,  by  \  the  \  large  \,  semicircle}{The \, number \, of  \, horizontal \, squrare  \, sides  \ cut  \,  by  \  the  \  large  \,  semicircle} )

\therefore \theta = 2\times tan^{-1}( \frac{10\cdot \sqrt{3} }{5\cdot \sqrt{3}} ) = 2.214

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A_{(segment \, of \, semicircle)} = \frac{1}{4} \times (2.214 - sin2.214) \times (11\cdot\sqrt{3} )^2 = 128.3 \, ft^2

Therefore; t

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