Answer:
16 cm.
Step-by-step explanation:
It is 4 times the ratio.
The correct answer is A -1.5
Given:
A figure of combination of hemisphere, cylinder and cone.
Radius of hemisphere, cylinder and cone = 6 units.
Height of cylinder = 12 units
Slant height of cone = 10 units.
To find:
The volume of the given figure.
Solution:
Volume of hemisphere is:
![V_1=\dfrac{2}{3}\pi r^3](https://tex.z-dn.net/?f=V_1%3D%5Cdfrac%7B2%7D%7B3%7D%5Cpi%20r%5E3)
Where, r is the radius of the hemisphere.
![V_1=\dfrac{2}{3}(3.14)(6)^3](https://tex.z-dn.net/?f=V_1%3D%5Cdfrac%7B2%7D%7B3%7D%283.14%29%286%29%5E3)
![V_1=\dfrac{6.28}{3}(216)](https://tex.z-dn.net/?f=V_1%3D%5Cdfrac%7B6.28%7D%7B3%7D%28216%29)
![V_1=452.16](https://tex.z-dn.net/?f=V_1%3D452.16)
Volume of cylinder is:
![V_2=\pi r^2h](https://tex.z-dn.net/?f=V_2%3D%5Cpi%20r%5E2h)
Where, r is the radius of the cylinder and h is the height of the cylinder.
![V_2=(3.14)(6)^2(12)](https://tex.z-dn.net/?f=V_2%3D%283.14%29%286%29%5E2%2812%29)
![V_2=(3.14)(36)(12)](https://tex.z-dn.net/?f=V_2%3D%283.14%29%2836%29%2812%29)
![V_2=1356.48](https://tex.z-dn.net/?f=V_2%3D1356.48)
We know that,
[Pythagoras theorem]
Where, l is length, r is the radius and h is the height of the cone.
![\sqrt{64}=h](https://tex.z-dn.net/?f=%5Csqrt%7B64%7D%3Dh)
Volume of cone is:
![V_3=\dfrac{1}{3}\pi r^2h](https://tex.z-dn.net/?f=V_3%3D%5Cdfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2h)
Where, r is the radius of the cone and h is the height of the cone.
![V_3=\dfrac{1}{3}(3.14)(6)^2(8)](https://tex.z-dn.net/?f=V_3%3D%5Cdfrac%7B1%7D%7B3%7D%283.14%29%286%29%5E2%288%29)
![V_3=\dfrac{25.12}{3}(36)](https://tex.z-dn.net/?f=V_3%3D%5Cdfrac%7B25.12%7D%7B3%7D%2836%29)
![V_3=301.44](https://tex.z-dn.net/?f=V_3%3D301.44)
Now, the volume of the combined figure is:
![V=V_1+V_2+V_3](https://tex.z-dn.net/?f=V%3DV_1%2BV_2%2BV_3)
![V=452.16+1356.48+301.44](https://tex.z-dn.net/?f=V%3D452.16%2B1356.48%2B301.44)
![V=2110.08](https://tex.z-dn.net/?f=V%3D2110.08)
Therefore, the volume of the given figure is 2110.08 cubic units.
Answer:
-14
Step-by-step explanation:
If you simplify the expression you get -14