Answer:
The volume of the figure is approximately 1244 in³
Step-by-step explanation:
The figure is formed by a rectangular prism and a hemisphere, therefore its total volume is formed by the the sum of the volume of each of these forms. The volume of a rectangular prism can be found by using the expression:
[tex]V_{rect} = length*width*height[/tex]
While the volume of a hemisphere is given by:
[tex]V_{hemis} = \frac{2}{3}*\pi*r^3[/tex]
The radius of the hemisphere is the difference between the total length of the figure and the length of the prism, therefore:
[tex]r = 17 - 11 = 6 \text{ in}[/tex]
We can now find the volume of the figure:
[tex]V = V_{rect} + V_{hemis}\\V = 11*6*12 + \frac{2}{3}*\pi*(6)^3\\V = 792 + 144*\pi\\V = 792 + 452.39\\V = 1244 \text{ in}^3[/tex]
