A disk of radius … can be covered by four strips of…

A disk of radius $1^{\prime \prime }$ can be covered by four strips of tape (width ${\frac{1}{2}}^{\prime \prime }$). If the strips are not parallel, prove that they can't cover the disk. Hint: Change to a unit sphere sliced by planes ${\frac{1}{2}}^{\prime \prime }$ apart. Problem 14 gives surface area $\pi$ for each slice.

This exercise builds on another exercise in its source book, which isn't shown here.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §8.3 Area of a Surface of Revolution, #22