Since the question explicitly stated that ice production is proportional to time, we're going to have to use proportion fractions. Remember to convert hours into minutes as well.
All you do is multiply 8 by 2.54, you get 20.32. Your answer is 20.32cm
Answer:
![Volume = 11488.21](https://tex.z-dn.net/?f=Volume%20%3D%2011488.21)
![Area = 2461.76](https://tex.z-dn.net/?f=Area%20%3D%202461.76)
Step-by-step explanation:
Given
![Radius, r = 14\ in](https://tex.z-dn.net/?f=Radius%2C%20r%20%3D%2014%5C%20in)
Shape: Sphere
Solving (a): The Volume
This is calculated as:
![Volume = \frac{4}{3}\pi r^3](https://tex.z-dn.net/?f=Volume%20%3D%20%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3)
Take
as 3.14 and substitute 14 for r
![Volume = \frac{4}{3} * 3.14 * 14^3](https://tex.z-dn.net/?f=Volume%20%3D%20%5Cfrac%7B4%7D%7B3%7D%20%2A%203.14%20%2A%2014%5E3)
![Volume = \frac{4}{3} * 3.14 * 2744](https://tex.z-dn.net/?f=Volume%20%3D%20%5Cfrac%7B4%7D%7B3%7D%20%2A%203.14%20%2A%202744)
![Volume = \frac{4 * 3.14 * 2744}{3}](https://tex.z-dn.net/?f=Volume%20%3D%20%5Cfrac%7B4%20%2A%203.14%20%2A%202744%7D%7B3%7D)
![Volume = \frac{34464.64}{3}](https://tex.z-dn.net/?f=Volume%20%3D%20%5Cfrac%7B34464.64%7D%7B3%7D)
![Volume = 11488.21](https://tex.z-dn.net/?f=Volume%20%3D%2011488.21)
Solving (b): The Surface Area
This is calculated as follows:
![Area = 4\pi r^2](https://tex.z-dn.net/?f=Area%20%3D%204%5Cpi%20r%5E2)
Take
as 3.14 and substitute 14 for r
![Area = 4 * 3.14 * 14^2](https://tex.z-dn.net/?f=Area%20%3D%204%20%2A%203.14%20%2A%2014%5E2)
![Area = 4 * 3.14 * 196](https://tex.z-dn.net/?f=Area%20%3D%204%20%2A%203.14%20%2A%20196)
![Area = 2461.76](https://tex.z-dn.net/?f=Area%20%3D%202461.76)
Step-by-step explanation:
Given that,
The height of the cone, h = 24 cm
The radius of the cone, r = 10 cm
The slant height of the cone is :
![l=\sqrt{h^2+r^2} \\\\l=\sqrt{24^2+10^2} \\\\l=26\ cm](https://tex.z-dn.net/?f=l%3D%5Csqrt%7Bh%5E2%2Br%5E2%7D%20%5C%5C%5C%5Cl%3D%5Csqrt%7B24%5E2%2B10%5E2%7D%20%5C%5C%5C%5Cl%3D26%5C%20cm)
The lateral area of the cone is given by :
![A=\pi rl\\\\=3.14\times 10\times 26\\\\=816.4\ cm^2\approx 816\ cm^2](https://tex.z-dn.net/?f=A%3D%5Cpi%20rl%5C%5C%5C%5C%3D3.14%5Ctimes%2010%5Ctimes%2026%5C%5C%5C%5C%3D816.4%5C%20cm%5E2%5Capprox%20816%5C%20cm%5E2)
The surface area of the cone is given by :
![A=2\pi rh\\\\=2\times 3.14\times 10\times 24\\\\=1507.2 \approx 1507\ cm^2](https://tex.z-dn.net/?f=A%3D2%5Cpi%20rh%5C%5C%5C%5C%3D2%5Ctimes%203.14%5Ctimes%2010%5Ctimes%2024%5C%5C%5C%5C%3D1507.2%20%5Capprox%201507%5C%20cm%5E2)
Use the poin-slope form of the equation of a line:-
y - y1 = m(x - x1) (where m = slope and the point is (x1, y1))
Plugging in the given values:-
y - 6 = 2/5(x - 10)
multiplying through by 5:-
5y - 30 = 2(x - 10)
5y - 30 = 2x - 20
5y = 2x + 10
In standard form the equation is
2x - 5y = -10 (answer)