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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Find the volume of the solid in the first octant bounded by the cylinder z = 16 − x2 and the plane y = 5.

To determine

To find: The volume of the solid in the first octant bounded by the cylinder.

Explanation

Formula used:

If g(x) is the function of x and h(y) is the function of y then,

abcdg(x)h(y)dydx=abg(x)dxcdh(y)dy (1)

The volume of the solid, V=RzdA , where, z is the given function.

Given:

The cylinder is z=16x2 .

The planes is y=5 .

Calculation:

Since the solid lies in the first octant, y varies from 0 to 5.

Moreover, x satisfies z for 4 and −4 and the solid lies in the first octant, x varies from 0 to 4.

So, the rectangular region is R=[0,4]×[0,5] .

Obtain the volume of the solid by using equation (1)

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Chapter 15 Solutions

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