A cone just fits inside a cylinder with volume of 300 cm cubed what is the volume of the cone

Find the area of the trapezoidal cross-section of the irrigation canal shown below. Your answer will be in terms of h, w, and θ.

miskamm [114]

[w + (h/tan θ)] × h

<h3>Further explanation</h3>

We aim is to find the area of the trapezoidal cross-section of the irrigation canal.

The formula for the area of the trapezoid is $\boxed{\boxed{ \ Area = \frac{1}{2} \times (a + b) \times h \ }}$

a & b = parallel sides
h = height

We assume the lower side is $\boxed{ \ a = w \ }$ and the upper side is b = x + w + x or $\boxed{ \ b = w + 2x \ }$ . See the attached picture.

In the right triangles located on the left and right of the trapezoid, we calculate the value of x based on trigonometric ratios namely tan of theta.

$\boxed{ \ tan \ \theta = \frac{opposite}{adjacent} \ }$

$\boxed{ \ tan \ \theta = \frac{h}{x} \ }$

$\boxed{ \ x = \frac{h}{tan \ \theta} \ }$

Substitute the equation of x to $\boxed{ \ b = w + 2x \ }.$

We get $\boxed{ \ b = w + \frac{2h}{tan \ \theta} \ }$

Finally all components are complete and can be substituted into a formula to calculate the area of a trapezoid.

$\circ \ \boxed{a = w}\\ \circ \ \boxed{ \ b = w + \frac{2h}{tan \ \theta} \ }\\\circ \ and \ h$

$\boxed{ \ Area = \frac{1}{2} \times (w + w + \frac{2h}{tan \ \theta}) \times h \ }$

$\boxed{ \ Area = \frac{1}{2} \times (2w + \frac{2h}{tan \ \theta}) \times h \ }$

$\boxed{ \ Area = \frac{1}{2} \times 2(w + \frac{h}{tan \ \theta}) \times h \ }$

Hence, the area of the trapezoidal cross-section of the irrigation canal is $\boxed{\boxed{ \ Area = (w + \frac{h}{tan \ \theta}) \times h \ }}$

<h3>Learn more</h3>

Find out the area of parallelogram brainly.com/question/4459688
The order of rotational symmetry of rhombus brainly.com/question/4228574
Find out the coordinates of the image of a point after the triangle is rotated 270° about the origin brainly.com/question/7437053

Keywords: the trapezoidal, cross-section of the irrigation canal, the area, the answer will be in terms of h, w, and θ, trigonometric ratios, tan, opposite, adjacent, height, sides

3 0

4 years ago

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(-7, -2) and (2, -9)

xxTIMURxx [149]

Answer:

-16

Step-by-step explanation:

3 0

3 years ago

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2x+3=39<br> Solve for x <br><br><br> Bjkkkvhihvcgjjvcgufufxgx

rodikova [14]

2x + 3 = 39

-3 -3

2x = 36

/2 /2

x = 18

7 0

3 years ago

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What kind of triangle has sides that have length 4, 8, and 10? ( the triangle acute, right, or obtuse ?)

dybincka [34]

Answer:

acute because your a cutie

Step-by-step explanation:

5 0

3 years ago

An insurer knows that the proportion of smokers in a population is 0.3. Furthermore, it is known that: 40% of applicants who are

olga nikolaevna [1]

<h3>Answer: Approximately 0.8537</h3>

===================================================

Explanation:

Let's say this population had 1000 people. You can pick any number you want, but I'm going for some nice big round number to work with.

The proportion of smokers is 0.3, which means 0.3*1000 = 300 people in this population are smokers and 1000-300 = 700 are nonsmokers.

Of the 300 people who do smoke, 40% of them lie on the application. This means 0.40*300 = 120 people lied. These 120 people say they don't smoke, but in fact they do smoke.

So if we were to survey this population, then 700+120 = 820 people would say they don't smoke

Only considering the people who write "don't smoke" on the survey, which is that 820 figure, 700 of them are true nonsmokers. Therefore, the probability we want is 700/820 = 0.8537 approximately

8 0

3 years ago