Answer:
a) ![SA = 522.9~cm^2](https://tex.z-dn.net/?f=SA%20%3D%20522.9~cm%5E2)
b) ![V_{cone} = 670.2~cm^3](https://tex.z-dn.net/?f=%20V_%7Bcone%7D%20%3D%20670.2~cm%5E3%20)
c) ![V_{empty} = 1340.4~cm^3](https://tex.z-dn.net/?f=%20V_%7Bempty%7D%20%3D%201340.4~cm%5E3%20)
Step-by-step explanation:
a)
For a cone,
![SA = \pi r (L + r)](https://tex.z-dn.net/?f=%20SA%20%3D%20%5Cpi%20r%20%28L%20%2B%20r%29%20)
where L = slant height
![L = \sqrt{r^2 + h^2}](https://tex.z-dn.net/?f=%20L%20%3D%20%5Csqrt%7Br%5E2%20%2B%20h%5E2%7D%20)
We have r = 8 cm; h = 10 cm
![L = \sqrt{(8~cm)^2 + (10~cm)^2}](https://tex.z-dn.net/?f=L%20%3D%20%5Csqrt%7B%288~cm%29%5E2%20%2B%20%2810~cm%29%5E2%7D)
![L = \sqrt{164~cm^2}](https://tex.z-dn.net/?f=L%20%3D%20%5Csqrt%7B164~cm%5E2%7D)
![SA = (\pi)(8~cm)(\sqrt{164~cm^2} + 8~cm)](https://tex.z-dn.net/?f=SA%20%3D%20%28%5Cpi%29%288~cm%29%28%5Csqrt%7B164~cm%5E2%7D%20%2B%208~cm%29)
![SA = 522.9~cm^2](https://tex.z-dn.net/?f=SA%20%3D%20522.9~cm%5E2)
b)
![V_{cone} = \dfrac{1}{3}\pi r^2 h](https://tex.z-dn.net/?f=%20V_%7Bcone%7D%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2%20h%20)
![V_{cone} = \dfrac{1}{3}(\pi)(8~cm)^2(10~cm)](https://tex.z-dn.net/?f=%20V_%7Bcone%7D%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%28%5Cpi%29%288~cm%29%5E2%2810~cm%29%20)
![V_{cone} = 670.2~cm^3](https://tex.z-dn.net/?f=%20V_%7Bcone%7D%20%3D%20670.2~cm%5E3%20)
c)
![V_{cylinder} = \pi r^2 h](https://tex.z-dn.net/?f=%20V_%7Bcylinder%7D%20%3D%20%5Cpi%20r%5E2%20h%20)
empty space = volume of cylinder - volume of cone
![V_{empty} = V_{cylinder} - V_{cone}](https://tex.z-dn.net/?f=%20V_%7Bempty%7D%20%3D%20V_%7Bcylinder%7D%20-%20V_%7Bcone%7D%20)
![V_{empty} = \pi r^2 h - \dfrac{1}{3}\pi r^2 h](https://tex.z-dn.net/?f=%20V_%7Bempty%7D%20%3D%20%5Cpi%20r%5E2%20h%20-%20%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2%20h%20)
![V_{empty} = (\pi)(8~cm)^2(10~cm) - \dfrac{1}{3}(\pi)(8~cm)^2(10~cm)](https://tex.z-dn.net/?f=%20V_%7Bempty%7D%20%3D%20%28%5Cpi%29%288~cm%29%5E2%2810~cm%29%20-%20%5Cdfrac%7B1%7D%7B3%7D%28%5Cpi%29%288~cm%29%5E2%2810~cm%29%20)
![V_{empty} = 1340.4~cm^3](https://tex.z-dn.net/?f=%20V_%7Bempty%7D%20%3D%201340.4~cm%5E3%20)
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Answer:138
Step-by-step explanation:
Answer:
The equation is true/ or an identity
Step-by-step explanation:
Plug in 7 for x, you get
2(7)+3=17
14+3=17
17=17