Question

The figure is made up of a hemisphere and a cone.

What is the exact volume of the figure.



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in3

Answer 1

Answer:

Volume of the figure = 2413.71 cubic inches.

Step-by-step explanation:

Volume of the figure = Volume of the hemisphere + Volume of the cone

= $\frac{2}{3} \pi r^{3} +\frac{1}{3} \pi r^{2} h$

$=\frac{1}{3} \pi r^{2} (2r + h)$

$=\frac{1}{3} (\frac{22}{7} )(8)(8)(16+20)$

$=\frac{22(8)(8)(12)}{7}$

= 2413.71 cubic inches.

Answer 2

Answer: $2411.52\ in^3$

Step-by-step explanation:

In the given figure, we have a hemisphere and cone with same radius = 8 in.

The volume of hemisphere is given by :-

$\text{Volume}=\frac{2}{3}\pi r^3\\\\\Rightarrow\text{Volume}=\frac{2}{3}(3.14)(8)^3\\\\\Rightarrow\text{Volume}=1071.78666667\ in^3$

For cone, the height of cone = 20 in.

The volume of cone is given by :-

$\text{Volume}=\frac{1}{3}\pi r^2h\\\\\Rightarrow\text{Volume}=\frac{1}{3}(3.14)(8)^2(20)\\\\\Rightarrow\text{Volume}=1339.73333333\ in^3$

Now, the exact volume of the figure

=Volume of cone+Volume of hemisphere

$=1071.78666667+1339.73333333=2411.52\ in^3$