Answer:
3,700
Step-by-step explanation:
I know it's black because I did it in my head
For me being 100% honest:
grade 9-11 no homework, pay attention in class and study night before.
Grade 12: pay attention more in class, do some homework when concepts hard, study night before.
Uni: Read notes, do class homework, read textbook, study week before.
Answer:
B and C are the same angles so if B is 60 so is C
Answer:
Volume of solid is ![\frac{40}{3}\pi](https://tex.z-dn.net/?f=%5Cfrac%7B40%7D%7B3%7D%5Cpi)
Step-by-step explanation:
We need to find the volume of solid formed by rotating the region bounded by the graph of
, y-axis and the line y=3 about the line y=5.
Please see the attachment for figure.
Using Shell method, ![V=\int_a^b\pi (R^2-r^2)dx](https://tex.z-dn.net/?f=V%3D%5Cint_a%5Eb%5Cpi%20%28R%5E2-r%5E2%29dx)
where,
a=0 (Lower limit of solid)
b=4 (Upper limit of solid)
(Outer Radius of Shell)
r=2 (Inner radius of shell)
dx is thickness of shell
Volume of shell, dV=Area of shell x Thickness
Volume of solid ![V=\int dV](https://tex.z-dn.net/?f=V%3D%5Cint%20dV)
![V=\int_0^4 \pi [(4-\sqrt{x})^2-2^2]dx](https://tex.z-dn.net/?f=V%3D%5Cint_0%5E4%20%5Cpi%20%5B%284-%5Csqrt%7Bx%7D%29%5E2-2%5E2%5Ddx)
![V=\int_0^4 \pi (16+x-8\sqrt{x}-4)dx](https://tex.z-dn.net/?f=V%3D%5Cint_0%5E4%20%5Cpi%20%2816%2Bx-8%5Csqrt%7Bx%7D-4%29dx)
![V=\pi (12x+\frac{x^2}{2}-\frac{16}{3}x^{3/2}|_0^4](https://tex.z-dn.net/?f=V%3D%5Cpi%20%2812x%2B%5Cfrac%7Bx%5E2%7D%7B2%7D-%5Cfrac%7B16%7D%7B3%7Dx%5E%7B3%2F2%7D%7C_0%5E4)
![V=\pi (48+8-\frac{128}{3})](https://tex.z-dn.net/?f=V%3D%5Cpi%20%2848%2B8-%5Cfrac%7B128%7D%7B3%7D%29)
![V=\frac{40}{3}\pi](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B40%7D%7B3%7D%5Cpi)
Thus, Volume of solid is ![\frac{40}{3}\pi](https://tex.z-dn.net/?f=%5Cfrac%7B40%7D%7B3%7D%5Cpi)