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Nataliya [291]
3 years ago
9

What is the volume of a hemisphere with a radius of 3.6m ,rounded to the nearest tenth of a cubic centimeter

Mathematics
1 answer:
Mrrafil [7]3 years ago
6 0

Answer:

V\approx 97.7\ m^3

Step-by-step explanation:

-A hemisphere is equivalent to half of a sphere.

- The area of a sphere is given by the formula:

V=\frac{4}{3}\pi r^3

-Given that r=3.6m, the hemisphere's volume can be calculated as:

V=\frac{4}{3}\pi r^3\\\\V_h=0.5\times \frac{4}{3}\pi r^3\\\\=0.5\times \frac{4}{3}\pi \times 3.6^3\\\\=97.7161\approx 97.7\ m^3

Hence, the hemisphere's volume is approximately  97.7\ m^3

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Answer:

The horizontal displacement is 11 units, the vertical displacement is 9 units, and the projection angle is 39.3 degrees.

Step-by-step explanation:

We can start using the definition of displacement in one dimension between any 2 points which is the difference between them, so we have

\Delta s = s_2-s_1

And apply it to get the horizontal and vertical displacements.

Once we have found them, we can use trigonometric functions to find the projection angle with respect the horizontal.

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Using the definition of displacement, we can write the horizontal displacement as

\Delta x = x_2-x_1

So we can use the given points P1:(x_1,y_2)  \text{  and  } P_2: (x_2,y_2) on the displacement formula

\Delta x = 15-4\\\Delta x = 11

In the same manner we can look at the y components of those points to find the vertical displacement

\Delta y = 17-8\\\Delta y =9

Thus the horizontal displacement is 11 units and the vertical displacement is 9 units.

Projection angle.

The projection angle with respect the horizontal is the angle that is made between the line that connects the points P1 and P2 and the horizontal, so we can use the linear displacements previously found to write

\tan(\theta) = \cfrac{\Delta y}{\Delta x}

Solving for the angle we get

\theta = \tan^{-1}\left(\cfrac{\Delta y}{\Delta x}\right)

Replacing values

\theta = \tan^{-1}\left(\cfrac{9}{11}\right)

Which give us

\theta = 39.3^\circ

So the projection angle is 39.3 degrees.

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