Geometry Examples with Answers

A light wave has a 670 nm wavelength in air. Its wavelength in a transparent solid is 420 nm. 
a. What is the light speed in this substance?
b. What is the light’s frequency in the solid?

A kite 100 ft above the ground moves horizontally at a speed of ${\displaystyle 8\frac{ft}{s}}$. When 200 feet of string have been released, how quickly does the angle between the string and the horizontal start to decrease?

A paper cup has the shape of a cone with height 10 cm and radius 3 cm (at the top). If water is poured into the cup at a rate of 2 cm^{3}/s, how fast is the water level rising when the water is 5 cm deep?

Determine the solid's volume inside each of the two spheres
${\displaystyle x^2+y^2+z^2+4x-2y+4z+5=0}$ 
and 
${\displaystyle x^2+y^2+z^2=4}$

A figure is made up of a triangle and a square, where the triangle's base $b_{\mathrm{△}}$ is a side of a square $l_{◻}$.
$h_{\mathrm{△}}$
$l_{\mathrm{△}}=s_{\mathrm{△}}$
$P_{figure}=56cm$
$A_{figure}=?$