Answer:
(x - 5)^2 + y^2 = 225/4,
or you could write it as (x - 5)^2 + y^2 = 56.25.
Step-by-step explanation:
The factor form is
(x - h)^2 + (y - k)^2 = r^2 where the center is (h, k) and r = the radius.
So we have:
(x - 5)^2 + (y - 0)^2 = r^2
As the point (-1, 9/2) is on the line:
(-1 - 5)^2 + (9/2)^2 = r^2
r^2 = 36 + 81/4
r^2 = 225/4.
So substituting for r^2:
(x - 5)^2 + (y - 0)^2 = 225/4
(x - 5)^2 + y^2 = 225/4 is the standard form.
Answer:
![\large\boxed{V=\dfrac{49\pi}{3}\ in^3}\approx51.29\ in^3}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7BV%3D%5Cdfrac%7B49%5Cpi%7D%7B3%7D%5C%20in%5E3%7D%5Capprox51.29%5C%20in%5E3%7D)
Step-by-step explanation:
The formula of a volume of a cone:
![V=\dfrac{1}{3}\pi r^2H](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2H)
r - radius
H - height
We have
r = (7 : 2) in = 3.5 in
H = 4 in
Substitute:
![V=\dfrac{1}{3}\pi(3.5)^2(4)=\dfrac{1}{3}\pi(12.25)(4)=\dfrac{49\pi}{3}\ in^3](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7B1%7D%7B3%7D%5Cpi%283.5%29%5E2%284%29%3D%5Cdfrac%7B1%7D%7B3%7D%5Cpi%2812.25%29%284%29%3D%5Cdfrac%7B49%5Cpi%7D%7B3%7D%5C%20in%5E3)
![\pi\approx3.14\\\\V\approx\dfrac{(49)(3.14)}{3}\approx51.29\ in^3](https://tex.z-dn.net/?f=%5Cpi%5Capprox3.14%5C%5C%5C%5CV%5Capprox%5Cdfrac%7B%2849%29%283.14%29%7D%7B3%7D%5Capprox51.29%5C%20in%5E3)