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Mrac [35]
4 years ago
8

The base of a solid is bounded by y=√(x), y=0, x=2, and x=6. Its cross-sections, taken perpendicular to the x-axis, are squares.

Find the volume of the solid in cubic units.

Mathematics
1 answer:
Gre4nikov [31]4 years ago
7 0

Answer:

8pi units³

Step-by-step explanation:

Volume of the solid

= pi × integral of y².dx

= pi × integral of x

pi × [x²/2]

Limits are x = 2 and x = 6

pi × [6²/2 - 2²/2]

pi × (18 - 2)

= 16pi units³

Since the solid is only above the x-axis half of this volume would be generated:

½ × 16pi = 8pi units³

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