Answer:
![\large\boxed{V=\dfrac{1,421\pi}{3}\ cm^3}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7BV%3D%5Cdfrac%7B1%2C421%5Cpi%7D%7B3%7D%5C%20cm%5E3%7D)
Step-by-step explanation:
We have the cone and the half-sphere.
The formula of a volume of a cone:
![V_c=\dfrac{1}{3}\pi r^2H](https://tex.z-dn.net/?f=V_c%3D%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2H)
r - radius
H - height
We have r = 7cm and H = (22-7)cm=15cm. Substitute:
![V_c=\dfrac{1}{3}\pi(7^2)(15)=\dfrac{1}{3}\pi(49)(15)=\dfrac{735\pi}{3}\ cm^3](https://tex.z-dn.net/?f=V_c%3D%5Cdfrac%7B1%7D%7B3%7D%5Cpi%287%5E2%29%2815%29%3D%5Cdfrac%7B1%7D%7B3%7D%5Cpi%2849%29%2815%29%3D%5Cdfrac%7B735%5Cpi%7D%7B3%7D%5C%20cm%5E3)
The formula of a volume of a sphere:
![V_s=\dfrac{4}{3}\pi R^3](https://tex.z-dn.net/?f=V_s%3D%5Cdfrac%7B4%7D%7B3%7D%5Cpi%20R%5E3)
R - radius
Therefore the formula of a volume of a half-sphere:
![V_{hs}=\dfrac{1}{2}\cdot\dfrac{4}{3}\pi R^3=\dfrac{2}{3}\pi R^3](https://tex.z-dn.net/?f=V_%7Bhs%7D%3D%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%5Cdfrac%7B4%7D%7B3%7D%5Cpi%20R%5E3%3D%5Cdfrac%7B2%7D%7B3%7D%5Cpi%20R%5E3)
We have R = 7cm. Substitute:
![V_{hs}=\dfrac{2}{3}\pi(7^3)=\dfrac{2}{3}\pi(343)=\dfrac{686\pi}{3}\ cm^3](https://tex.z-dn.net/?f=V_%7Bhs%7D%3D%5Cdfrac%7B2%7D%7B3%7D%5Cpi%287%5E3%29%3D%5Cdfrac%7B2%7D%7B3%7D%5Cpi%28343%29%3D%5Cdfrac%7B686%5Cpi%7D%7B3%7D%5C%20cm%5E3)
The volume of the given shape:
![V=V_c+V_{hs}](https://tex.z-dn.net/?f=V%3DV_c%2BV_%7Bhs%7D)
Substitute:
![V=\dfrac{735\pi}{3}+\dfrac{686\pi}{3}=\dfrac{1,421\pi}{3}\ cm^3](https://tex.z-dn.net/?f=V%3D%5Cdfrac%7B735%5Cpi%7D%7B3%7D%2B%5Cdfrac%7B686%5Cpi%7D%7B3%7D%3D%5Cdfrac%7B1%2C421%5Cpi%7D%7B3%7D%5C%20cm%5E3)
Answer:
X<7. Graph 7. Then put a open circle and arrow it going left! And there you go.
Step-by-step explanation:
Add 18 to both sides. Since -2x has a negative, you flip the sign to less than instead of greater than.
Answer:
Step-by-step explanation:
volume=3×3×7=63 inch³
Answer:
5 km
Step-by-step explanation:
the scans means that any distance on the map is 50000 times larger in real life.
so, 10 cm on the map is
10×50000 = 500000 cm in real life.
now, we know that 100cm = 1 m
so, it is 500000/100 = 5000 m in real life.
and there are 1000 m in 1 km.
so, it is 5000/1000 = 5 km in real life