The volume
of a cone with base radius
and height
is
![V_c = \dfrac{1}{3}\pi r_c^2 h_c](https://tex.z-dn.net/?f=V_c%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20r_c%5E2%20h_c)
Similarly, the volume
of a sphere with radius
is
![V_s = \dfrac{4}{3}\pi r_s^3](https://tex.z-dn.net/?f=V_s%20%3D%20%5Cdfrac%7B4%7D%7B3%7D%5Cpi%20r_s%5E3)
We know that
and that ![h_c=96](https://tex.z-dn.net/?f=h_c%3D96)
So, we can set up the following equation:
![\dfrac{96}{3}\pi r_c^2=\dfrac{4}{3}\pi r_s^3](https://tex.z-dn.net/?f=%5Cdfrac%7B96%7D%7B3%7D%5Cpi%20r_c%5E2%3D%5Cdfrac%7B4%7D%7B3%7D%5Cpi%20r_s%5E3)
We can simplify the common denominator 3, and pi appearing on both sides:
![96r_c^2=4r_s^3](https://tex.z-dn.net/?f=96r_c%5E2%3D4r_s%5E3)
We can divide both sides by 4:
![24r_c^2=r_s^3](https://tex.z-dn.net/?f=24r_c%5E2%3Dr_s%5E3)
Without further information, this is all we can say: the cubed radius of the sphere is the same as 24 times the squared radius of the cone.
Answer:
8 units
Step-by-step explanation:
» <u>Concepts</u>
Parallelogram Side Theorem states that the opposite sides of a parallelogram are congruent, meaning they have the same length.
» <u>Application</u>
In this case, we're asked to apply the theorem to find the value of q and then find the length of AB. Thus, we have to set up the equation 4q - 8 = q + 4.
» <u>Solving</u>
Step 1: Subtract q from both sides.
Step 2: Add 8 to both sides.
Step 3: Divide both sides by 3.
Step 4: Plug in the value of q for side AB.
Therefore, the answer is 8 units.
The Square Root Of 8100 Is 90. That Will Be The Only Square Root Because The Square Root Of 90 Is A Decimal So You Would Stop There.
The factors of 16 are 1, 2, 4, 8, and 16.
<span>The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. </span>
<span>The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. </span>
<span>So the greatest common factor of 16, 24, and 40 is 8.
Hope this helps:)</span>
Answer:
8 hours
Step-by-step explanation:
pretty sure
6 hours is in half and 10 hours is in half add it up and you get 8?