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find the volume of the backpack that is 17” x 12” x 4”. i would solve using l x w x h, but there is a hemisphere or something on top! very confused

thanks in advance!

find the volume of the backpack that is 17 x 12 x 4 i would solve using l x w x h but there is a hemisphere or something on top very confused thanks in advance class=

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MathPhys

Answer:

V = 528 + 72π

V ≈ 754.2 in³

Step-by-step explanation:

The width of the backpack is also the diameter of the semicylinder.  So the radius of the semicylinder is r = 6 in.  Which means the height of the rectangular prism is h = 17 in − 6 in = 11 in.

The total volume is the volume of the rectangular prism + the volume of the semicylinder.

V = LWH + ½ (π R² L)

V = (4)(12)(11) + ½ π (6)² (4)

V = 528 + 72π

V ≈ 754.2 in³

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