Find the volume of the solid formed when the shaded region

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Reference no: EM131212210

1. Find the volume of the solid formed when the shaded region is revolved about the indicated axis.

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2. Find the volume of the solid generated by revolving the region bounded by y = x (1 +x3)1/4 over 0 ≤ x ≤ 1 about the x-axis.

3. A city's water storage tank is in the shape of the solid of revolution generated by revolving the region under the graph of f(x)= 50 √(1 - x2/1600) from x = -40 feet to x = 40 feet about the x-axis.

(a) What is the volume of this tank?

(b) It is known that 1 ft3 hold 7.48 gallons. How much water does this tank hold?

4. Find the volume of the solid that results when the region enclosed by y = sin(x), y = cos(x), x = 0, x = π/4 is revolved about the x-axis. [Hint: Use a trigonometric identity to simplify the integrand.]

5. Let V be the volume of the solid that results when the region enclosed by y = 1/x, y = 0, x = b, and x = 2 (0 < b < 2) is revolved about the x-axis. Find the value of b for which V = 3.

Reference no: EM131212210

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