Answer:
Part A) The volume of the entire cone is ![168\pi\ in^3](https://tex.z-dn.net/?f=168%5Cpi%5C%20in%5E3)
Part B) see the explanation
Step-by-step explanation:
Part A) we know that
The volume of a cone is equal to
![V=\frac{1}{3}\pi r^{2}h](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E%7B2%7Dh)
where
r is the radius of the base of the cone
h is the height of the cone
In this problem triangle ABD is similar to triangle ACE
Remember that If two figures are similar, then the ratio of its corresponding sides is proportional
so
![\frac{AB}{AC}=\frac{BD}{CE}](https://tex.z-dn.net/?f=%5Cfrac%7BAB%7D%7BAC%7D%3D%5Cfrac%7BBD%7D%7BCE%7D)
substitute the given values
![\frac{7}{14}=\frac{3}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B14%7D%3D%5Cfrac%7B3%7D%7Bx%7D)
solve for x
![x=14(3)/7\\x=6\ in](https://tex.z-dn.net/?f=x%3D14%283%29%2F7%5C%5Cx%3D6%5C%20in)
To find out the volume of the entire cone we have
![r=CE=x=6\ in](https://tex.z-dn.net/?f=r%3DCE%3Dx%3D6%5C%20in)
![h=AC=14\ in](https://tex.z-dn.net/?f=h%3DAC%3D14%5C%20in)
substitute in the formula
![V=\frac{1}{3}\pi (6)^{2}(14)](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%286%29%5E%7B2%7D%2814%29)
![V=168\pi\ in^3](https://tex.z-dn.net/?f=V%3D168%5Cpi%5C%20in%5E3)
Part B) How did you determine the value for x in triangle ACE
In this problem triangle ABD is similar to triangle ACE
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
so
![\frac{AB}{AC}=\frac{BD}{CE}](https://tex.z-dn.net/?f=%5Cfrac%7BAB%7D%7BAC%7D%3D%5Cfrac%7BBD%7D%7BCE%7D)
substitute the given values and solve for x
Answer:
right angle triangle 90 degrees
scute less than 90 degrees
obtuse over 90 degrees
Step-by-step explanation:
Answer:
900m
Step-by-step explanation:
So your base is -400m so what you want to do is add up till you get to 0. So you add 400m to get to zero. Then you need to subtract from 500m until you get to 0. So you have 500m. Then you add 400m and 500m (400m+500m) which gives you the answer 900m.
Answer:
x = 15
arc PQ = 110°
ΔPQR is an acute triangle
Step-by-step explanation:
(6x) + (8x-10) + (10x+10) = 360°
combine like terms:
24x = 360°
x = 15
arc PQ = 8(15) - 10° = 110°
Answer:
A and C
Step-by-step explanation:
You will have both a vertical stretch and a horizontal compression