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Answer:
The height of the building is approximately <u>73 m</u>.
Step-by-step explanation:
The triangle EFG is shown below.
Given:
Length of shadow of building is,
Angle of inclination of Sun with the vertical is 25°.
Therefore, the angle of inclination of Sun with the horizontal is given as:
Now, in triangle EFG as shown below, we use the tangent ratio to determine the height of building EF. Therefore,
Therefore, the height of the building is approximately 73 m.
<em>x</em> ^2 + <em>y</em> ^2 = 9 => <em>y</em> = <em>y(x)</em> = ± √(9 - <em>x</em> ^2)
Each cross section would be a square with side length equal to the vertical distance between the upper and lower semicircles defined by <em>y(x)</em>, which is
√(9 - <em>x</em> ^2) - (- √(9 - <em>x</em> ^2)) = 2 √(9 - <em>x</em> ^2)
The area of each square section is the square of this length,
(2 √(9 - <em>x</em> ^2)) = 4 (9 - <em>x</em> ^2) = 36 - 4<em>x</em> ^2
We get the whole solid for -3 ≤ <em>x</em> ≤ 3, so integrating gives a volume of