Answer:
The volume of the toy is ![V=5.23\ ft^3](https://tex.z-dn.net/?f=V%3D5.23%5C%20ft%5E3)
Step-by-step explanation:
step 1
Find the volume of the hemisphere
The volume of the hemisphere is given by the formula
![V=\frac{2}{3}\pi r^{3}](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B2%7D%7B3%7D%5Cpi%20r%5E%7B3%7D)
In this problem, the wide of the toy is equal to the diameter of the hemisphere
so
![D=2\ ft](https://tex.z-dn.net/?f=D%3D2%5C%20ft)
----> the radius is half the diameter
substitute
![V=\frac{2}{3} \pi (1)^{3}=\frac{2}{3} \pi\ ft^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B2%7D%7B3%7D%20%5Cpi%20%281%29%5E%7B3%7D%3D%5Cfrac%7B2%7D%7B3%7D%20%5Cpi%5C%20ft%5E3)
step 2
Find the volume of the cone
The volume of the cone is given by
![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)
we know that
The radius of the cone is the same that the radius of the hemisphere
so
![r=1\ ft](https://tex.z-dn.net/?f=r%3D1%5C%20ft)
The height of the cone is equal to subtract the radius of the hemisphere from the height of the toy
![h=4-1=3\ ft](https://tex.z-dn.net/?f=h%3D4-1%3D3%5C%20ft)
substitute the given values
![V=\frac{1}{3}\pi (1)^{2}(3)=\pi\ ft^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%281%29%5E%7B2%7D%283%29%3D%5Cpi%5C%20ft%5E3)
step 3
Find the volume of the toy
we know that
The volume of the toy, is equal to the volume of the cone plus the volume of the hemisphere.
so
![V=(\frac{2}{3} \pi+\pi)\ ft^3](https://tex.z-dn.net/?f=V%3D%28%5Cfrac%7B2%7D%7B3%7D%20%5Cpi%2B%5Cpi%29%5C%20ft%5E3)
![V=(\frac{5}{3}\pi)\ ft^3](https://tex.z-dn.net/?f=V%3D%28%5Cfrac%7B5%7D%7B3%7D%5Cpi%29%5C%20ft%5E3)
assume
![\pi=3.14](https://tex.z-dn.net/?f=%5Cpi%3D3.14)
![V=\frac{5}{3}(3.14)=5.23\ ft^3](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B5%7D%7B3%7D%283.14%29%3D5.23%5C%20ft%5E3)
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Step-by-step explanation:
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Answer:
6
Step-by-step explanation:
To solve for x you must isolate it.
3x-2=2x+4
-2x -2x Subtract 2x from both sides
x-2=4 Your left with this
+2 +2 Then add 2 to both sides
x=6 x equals to 6
The rule is to add 5/6. so the unknown term should be 4 1/3 because 3 1/2 + 5/6 = 4 1/3