A cylinder fits inside a square prism as shown. For Every cross section, the ratio of the area of the circle to the area of the square is pir2/4r2 or pi/4. Since the area of the circles is pi/4 the area of the Square, the volume of the cylinder equals

1. Pi/2 The volume of the prism or pi/2 (2r)(h) or pi rh

2. Pi/2 the volume of the prism or pi/2 (4r2)(h) or 2r2h

3. Pi/4 The volume of the prism or pi/4 (2r)(h) or pi/4r2h

4. Pi/4 The volume of the prism or pi/4 (4r2)(h) or pi r2h

Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x^2 + 3x + 4, [−1, 1] no, f is continuous on [−1, 1] but not differentiable on (−1, 1). no, f is not continuous on [−1, 1]. yes, f is continuous on [−1, 1] and differentiable on (−1, 1) since polynomials are continuous and differentiable on . there is not enough information to verify if this function satisfies the mean value theorem. yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem.