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Mathematics

1 answer:

vazorg [7]2 years ago

4 0

If you find the volume of each figure separately then add them together, then you'd get your answer.

The formula for volume is V=Base Area*Height, V=BH
So the volume of the smaller cube is 210.
This is because the base area is 15*14. Multiply this by the height, 16, then you get 210.

The volume of the second cube is 25,100. This is because 15+16 is 31. 31*27*30 is 25,100.

If you add both of these volumes together, you're final answer is 25,310 units cubed.

Hope this helped :)

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Answer is option d)346.4 ft

Step-by-step explanation:

$from \: the \: figure \\ AB = 300 \: ft \: \: \: angle \: C = 60 \:( theta)\: degress \\ in \: triangle \: ABC \: using \: tan \: theta\\ \tan(60) = \frac{opposite \: side}{adjacent \: side} \\ \tan(60) = \frac{300}{BC} \\ \sqrt{3} = \frac{300}{BC} \\ BC = \frac{300}{ \sqrt{3} } \\ BC = 100 \sqrt{3} ft \\ then \: in \: triangle \: ABD \: using \: tan \: theta \\ angle \: D = 30 \: degrees \: (theta) \\ \tan(30 ) =\frac{opposite \: side}{adjacent \: side} \\ \tan(30) = \frac{300}{BD} \\ \frac{1}{ \sqrt{ 3} } = \frac{300}{BD} \\ BD = 300 \sqrt{3} \\ CD = BD - BC \\ = 300 \sqrt{3 } - 100 \sqrt{3} \\ = (300 - 100) \sqrt{3} \\ = 200 \sqrt{3 } \\ = 200 \times 1.732 \\ = 346.4 \: ft$

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2 years ago