Answer:
47.3 m³
Step-by-step explanation:
The garden shed is made up of a rectangular prism and a pyramid.
<h3><u>Volume of a rectangular prism</u></h3>
![\begin{aligned}\textsf{Volume of a rectangular prism}&=\sf width \times length \times height\\&=4 \times 4 \times 2\\&=16 \times 2\\&=32\;\; \sf m^3\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Ctextsf%7BVolume%20of%20a%20rectangular%20prism%7D%26%3D%5Csf%20width%20%5Ctimes%20length%20%5Ctimes%20height%5C%5C%26%3D4%20%5Ctimes%204%20%5Ctimes%202%5C%5C%26%3D16%20%5Ctimes%202%5C%5C%26%3D32%5C%3B%5C%3B%20%5Csf%20m%5E3%5Cend%7Baligned%7D)
<h3><u>Volume of a pyramid</u></h3>
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From inspection of the given diagram, the slant height of the pyramid is 3.5 m.
Calculate the perpendicular height of the pyramid using Pythagoras Theorem:
![\begin{aligned}\implies a^2+b^2&=c^2\\2^2+h^2&=3.5^2\\h^2&=8.25\\h&=\sqrt{8.25}\;\; \sf m\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cimplies%20a%5E2%2Bb%5E2%26%3Dc%5E2%5C%5C2%5E2%2Bh%5E2%26%3D3.5%5E2%5C%5Ch%5E2%26%3D8.25%5C%5Ch%26%3D%5Csqrt%7B8.25%7D%5C%3B%5C%3B%20%5Csf%20m%5Cend%7Baligned%7D)
Therefore:
![\begin{aligned}\textsf{Volume of a pyramid}&=\dfrac{\sf length \times width \times height}{3}\\\\&=\dfrac{\sf 4 \times 4 \times \sqrt{8.25}}{3}\\\\& = 15.31883372\;\; \sf m^3\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Ctextsf%7BVolume%20of%20a%20pyramid%7D%26%3D%5Cdfrac%7B%5Csf%20length%20%5Ctimes%20width%20%5Ctimes%20height%7D%7B3%7D%5C%5C%5C%5C%26%3D%5Cdfrac%7B%5Csf%204%20%5Ctimes%204%20%5Ctimes%20%5Csqrt%7B8.25%7D%7D%7B3%7D%5C%5C%5C%5C%26%20%3D%2015.31883372%5C%3B%5C%3B%20%5Csf%20m%5E3%5Cend%7Baligned%7D)
<h3><u>Volume of the garden shed</u></h3>
![\begin{aligned}\implies \textsf{Volume of shed}&=\textsf{Volume of rectangular prism}+\textsf{Volume of pyramid}\\&=32+15.31883372\\& = 47.3\;\; \sf m^3\;(nearest\;tenth)\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cimplies%20%5Ctextsf%7BVolume%20of%20shed%7D%26%3D%5Ctextsf%7BVolume%20of%20rectangular%20prism%7D%2B%5Ctextsf%7BVolume%20of%20pyramid%7D%5C%5C%26%3D32%2B15.31883372%5C%5C%26%20%3D%2047.3%5C%3B%5C%3B%20%5Csf%20m%5E3%5C%3B%28nearest%5C%3Btenth%29%5Cend%7Baligned%7D)
Data:
surface area=324 m²
lenght=5 m
width=12 m
SA=2(Iw+Ih+wh)
324 m²=2(5 m*12 m + 5 m h+12 m h)
324 m²=2(60 m²+17 m h)
60 m²+17 mh=324 m²/2
60 m²+17 mh=162 m²
17 mh=162 m²-60 m²
17 mh=102 m²
h=102 m²/17 m
h=6 m
Answer: the height is 6 m
Answer:
19 birds where there on Friday
Answer:
![log_{3}(x-4)= 3log_{3}(2)](https://tex.z-dn.net/?f=log_%7B3%7D%28x-4%29%3D%203log_%7B3%7D%282%29)
Step-by-step explanation:
The given equation is:
![x-4=2^{3}](https://tex.z-dn.net/?f=x-4%3D2%5E%7B3%7D)
We have to find the logarithmic equation with same solution as the given equation.
If we take the log of both sides, we can get a logarithmic equation. Since the log operation is applied to both sides the solution of the equation will stay the same.
Taking the logarithm to the base 3 of both sides, we get:
![log_{3}(x-4)= log_{3}(2)^{3}\\\\ log_{3}(x-4)= 3log_{3}(2)](https://tex.z-dn.net/?f=log_%7B3%7D%28x-4%29%3D%20log_%7B3%7D%282%29%5E%7B3%7D%5C%5C%5C%5C%20log_%7B3%7D%28x-4%29%3D%203log_%7B3%7D%282%29)