(PLSSS HELP!!) Explain how the formula for the area of a square is related to the formula for the volume of a cube.

Mathematics

1 answer:

Serga [27]3 years ago

5 0

x = side length

Area of a square = x^2

Area of a cube = x^3

The squaring operation is directly tied to the geometric shape of a square. The naming is not a coincidence. The same can be said about the cubing exponent being connected to a 3D cube in geometry.

Notice how x^3 can be written as x^2*x. Buried inside the volume of a cube formula is the area of a square. We can effectively rewrite that second equation as

volume of a cube = (area of a square)*x

where x is the side length of the cube and square

This idea of tying together the volume and area like this will be helpful when setting up other volume formulas (eg: volume of a prism).

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Convert (5, pi/6) to rectangular coordinates

kupik [55]

Polar coordinates are written as the distance of the point to the origin and its angle of elevation around the unit cirlce.

Draw a right triangle with an angle of $\frac{\pi}6$ and a hypotenuse with a length of 5.

You can use trigonometric ratios to find the legs of this triangle, which are the x and y coordinates of the point.

$\cos=\frac{adj}{hyp} \\\\ \cos(\frac{\pi}6)=\frac{x}5 \\\\ \frac{\sqrt{3}}2=\frac{x}5 \\\\ \frac{5\sqrt{3}}2=x$

As for y...

$\sin=\frac{opp}{hyp}\\\\\sin(\frac{\pi}6) = \frac{y}5 \\\\ \frac{1}2=\frac{y}5 \\\\ \frac{5}2=y$

$\boxed{(\frac{5\sqrt{3}}2,\ \frac{5}2)}$