\[\begin{array}{1 1}(1)100\pi&(2)\frac{100}{9}\pi\\(3)\frac{100}{3}\pi&(4)\frac{100}{3}\end{array}\]

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Required volume $V= \int \limits_a^b \pi y^2 dx$

$\qquad= \pi \int \limits_0^4 (3+x^2) dx$

$\qquad= \pi [3x+\large\frac{x^2}{3} ]^4_0$

$\qquad= \pi [3(4-0) +\large\frac{1}{3}$$ (4^3 -0)]$

$\qquad= \pi [12 +\large\frac{64}{3}]$

$\qquad = \pi [ \large\frac{36+64}{3}]=\frac{100}{3}$$\pi$

Hence 3 is the correct answer.

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