GJ is a tangent
АG is a radius
A tangent line to a circle is perpendicular to the radius drawn to the tangent point ⇒ m∠АGJ = 90° ⇒ ΔАGJ is the right triangle.
<span>By the Pythagorean theorem:
</span>AJ² = АG² + GJ²
AJ² = 9² + 12² = 81 + 144 = 225
AJ = √225 = 15 units.
What’s something goes up but never comes down?
a)
Check the picture below.
b)
volume wise, we know the smaller pyramid is 1/8 th of the whole pyramid, so the volume of the whole pyramid must be 8/8 th.
Now, if we take off 1/8 th of the volume of whole pyramid, what the whole pyramid is left with is 7/8 th of its total volume, and that 7/8 th is the truncated part, because the 1/8 we chopped off from it, is the volume of the tiny pyramid atop.
Now, what's the ratio of the tiny pyramid to the truncated bottom?
Answer:
first box is 4/5 and the second box (=) is 7/15