Plot[ {Cos[x],Sec[x]^2}, {x,0,Pi/4}, AspectRatio->Automatic]

Volume = height (4 inches) times cross-section area

Integrate[ Sec[x]^2 - Cos[x], {x,0,Pi/4}]

N[1-(1/(Sqrt[2]))]

4 * 0.29289321881345254

(If you  had to do this by hand, recall that secant squared is the derivative of tangent, so the antiderivative of secant squared must be tangent.)

Integrate[ Sec[x]^2, x ]

“Between curves x^2 and 1-x^2”

Plot[ {x^2, 1-x^2}, {x,-3, 3} ]

Plot3D[ Sin[x]*Cos[y], {x,-2Pi,2Pi}, {y,-2Pi,2Pi}]