(MIDDLE SCHOOL MATH) what numbers go on the y axis? What should I count by?
1 answer:
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You know that 
so 
.
Area of a shaded region is:
![$A=\int\limits_0^k\dfrac{y^2}{4}\,dy=\frac{1}{4}\int\limits_0^ky^2\,dy=\frac{1}{4}\left[\frac{y^3}{3}\right]_0^k=\frac{1}{4}\left[\frac{k^3}{3}-\frac{0^3}{3}\right]=\frac{1}{4}\cdot\dfrac{k^3}{3}=\boxed{\frac{k^3}{12}}](https://tex.z-dn.net/?f=%24A%3D%5Cint%5Climits_0%5Ek%5Cdfrac%7By%5E2%7D%7B4%7D%5C%2Cdy%3D%5Cfrac%7B1%7D%7B4%7D%5Cint%5Climits_0%5Eky%5E2%5C%2Cdy%3D%5Cfrac%7B1%7D%7B4%7D%5Cleft%5B%5Cfrac%7By%5E3%7D%7B3%7D%5Cright%5D_0%5Ek%3D%5Cfrac%7B1%7D%7B4%7D%5Cleft%5B%5Cfrac%7Bk%5E3%7D%7B3%7D-%5Cfrac%7B0%5E3%7D%7B3%7D%5Cright%5D%3D%5Cfrac%7B1%7D%7B4%7D%5Ccdot%5Cdfrac%7Bk%5E3%7D%7B3%7D%3D%5Cboxed%7B%5Cfrac%7Bk%5E3%7D%7B12%7D%7D%20)
so k:
![\dfrac{k^3}{12}=\dfrac{9}{4}\\\\\\k^3=\dfrac{9\cdot12}{4}\\\\\\k^3=9\cdot3\\\\k^3=3^3\quad|\sqrt[3]{(\ldots)}\\\\\boxed{k=3}](https://tex.z-dn.net/?f=%5Cdfrac%7Bk%5E3%7D%7B12%7D%3D%5Cdfrac%7B9%7D%7B4%7D%5C%5C%5C%5C%5C%5Ck%5E3%3D%5Cdfrac%7B9%5Ccdot12%7D%7B4%7D%5C%5C%5C%5C%5C%5Ck%5E3%3D9%5Ccdot3%5C%5C%5C%5Ck%5E3%3D3%5E3%5Cquad%7C%5Csqrt%5B3%5D%7B%28%5Cldots%29%7D%5C%5C%5C%5C%5Cboxed%7Bk%3D3%7D)
Area of a shaded region is:
so k:
Answer:
Volume = 42.8 cubic centimeters
Step-by-step explanation:
The volume of right circular cone is:
Where
r is the radius
h is the height
We are given height of 9.1 cm
h = 9.1
We aren't given radius explicitly, we are given circumference of 13.3, so we need to figure out radius from that. Lets do this:
So,
r = 2.12
Now, substituting in cone formula, we get the volume to be:
Rounded to nearest 10th is 1 decimal place, so
<u>Volume = 42.8 cubic centimeters</u>