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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.

The base of a solid is bounded by yx y0 x2 and x6 Its crosssections taken perpendicular to the xaxis are squares Find the volume of the solid in cubic units class=

Respuesta :

amna04352

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

kapoorprachi783

The answer is 8pi units³.

How to find volume?

The 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

What is a volume?

The amount of space occupied by a three-dimensional figure as measured in cubic units.

Learn more about volume here: brainly.com/question/1972490

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