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statuscvo [17]
3 years ago
9

Any help would be appreciated ❤ ❤ Thank you

Mathematics
1 answer:
Paladinen [302]3 years ago
7 0
The solid shape is a cone and a half sphere. So the equation would be (cone volume) + (1/2 sphere volume):
cone =  \frac{1}{3} \pi {r}^{2} h \\ sphere =  \frac{4}{3} \pi {r}^{3}  \\ object = ( \frac{1}{3} \pi  {r}^{2} h) +  \frac{1}{2} ( \frac{4}{3} \pi  {r}^{3} )
If the volume of the cone is 270pi and the height of the cone is 10, then:
270\pi =  \frac{1}{3} \pi {r}^{2} (10) \\ 27 =  \frac{1}{3}  {r}^{2}  \\ 80 =  {r}^{2}  \\ r = 9
The radius of the object is 9 cm. Therefore, we can plug into the formula for the total volume:
object = 270\pi +  \frac{1}{2} ( \frac{4}{3} \pi {(9)}^{3} ) \\  = 270\pi +  \frac{2}{3} (729\pi) \\  = 270\pi \: + 243\pi \\  = 513\pi
The total volume is 513 pi cm^3
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