Answer:
![3.14r^2(h-\frac{1}{3}h_1)](https://tex.z-dn.net/?f=3.14r%5E2%28h-%5Cfrac%7B1%7D%7B3%7Dh_1%29)
Step-by-step explanation:
Let h be the cylinders height and r the radius.
-The volume of a cylinder is calculated as:
![V=\pi r^2h](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E2h)
-Since the cone is within the cylinder, it has the same radius as the cylinder.
-Let
be the height of the cone.
-The area of a cone is calculated as;
![V=\pi r^2 \frac{h}{3}\\\\=\frac{1}{3}\pi r^2h_1](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E2%20%5Cfrac%7Bh%7D%7B3%7D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2h_1)
The volume of the solid section of the cylinder is calculated by subtracting the cone's volume from the cylinders:
![V=V_{cy}-V_{co}\\\\=\pi r^2h-\frac{1}{3}\pi r^2 h_1, \pi=3.14\\\\=3.14r^2(h-\frac{1}{3}h_1)](https://tex.z-dn.net/?f=V%3DV_%7Bcy%7D-V_%7Bco%7D%5C%5C%5C%5C%3D%5Cpi%20r%5E2h-%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2%20h_1%2C%20%5Cpi%3D3.14%5C%5C%5C%5C%3D3.14r%5E2%28h-%5Cfrac%7B1%7D%7B3%7Dh_1%29)
Hence, the approximate area of the solid portion is ![3.14r^2(h-\frac{1}{3}h_1)](https://tex.z-dn.net/?f=3.14r%5E2%28h-%5Cfrac%7B1%7D%7B3%7Dh_1%29)
From the Special Triangle Theorem, the hypotenuse is equal to the side lengtht times the Sqrt(2).
So hypotenuse H = xSqrt(2), x=H/Sqrt(2).
Using numbers, if H = 7, then x = 7/Sqrt(2) = 7Sqrt(2)/2 to rationalize it.
Answer:
A
Step-by-step explanation:
Answer:
64π inches² (approximately 201.06 inches²)
Step-by-step explanation:
where
is the radius
To find the radius, divide the diameter by 2
16 ÷ 2 = 8 inches
Plug in 8 as the radius
![A=\pi (8)^2\\A=64\pi](https://tex.z-dn.net/?f=A%3D%5Cpi%20%288%29%5E2%5C%5CA%3D64%5Cpi)
(approximately)
Therefore, the area of the circle is 64π inches², or approximately 201.06 inches².
I hope this helps!