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
Okay so-
you need to figure out how much one costs 10.50/2= 5.25
then you multiply by 5
5*5.25= 26.25
she’d spend $26.25
Answer:
a) 4/7 L = 0.57 L
b) 25/7 L = 3.57 L
Step-by-step explanation:
The ratio of orange juice to ginger ale is 2:5.
Add 2 + 5 = 7.
The ratio of orange juice to ginger ale to total drink is 2:5:7.
a) The fraction of orange juice is 2/7 of the total drink.
To make 2 L, you will need 2/7 of 2 L to be orange juice.
2/7 * 2 L = 4/7 L = 0.57 L
b) The fraction of ginger ale is 5/7 of the total drink.
5/7 * 5 L = 25/7 L = 3.57 L
Answer:
684in^2
Step-by-step explanation:
90/18 equals 5 minutes for each window,so after 3 hours they would paint 36 windows. 180 minutes in three hours so 180/5=36