Question 1
As shown in Figure 1, there are three different slopes which are formed from three mutually tangent circular arcs: a quarter-circle of radius $21$ cm, followed by a quarter-circle of radius $35$ cm, followed by a semicircle of radius $21$ cm. As shown in Figure 2, a disk of radius $7$ cm rolls along the slope from the left endpoint to the right endpoint, without slipping and always remaining tangent to the slope. What is the total area, in $\mathrm{cm}^2$, of the region covered by the disk as it rolls along the slope? (Note: Take $\pi=\frac{22}{7}$.)
Figure 1 is on the left; Figure 2 is on the right. The solid disks mark the starting and ending positions.
Figure 1 is on the left; Figure 2 is on the right. The solid disks mark the starting and ending positions.