**Question 1: **Find the area of cross section, when a cylinder is cut vertically parallel to the base, whose radius is 3 cm and height is 25 cm.

** Solution: **
Given: The cylinder is cut vertically. This means the obtained figure will be a circle.

Area of a circle is $\pi$ $\times$ r$^{2}$

Given: radius = 3 cm

So, the area of cross section = 3.14 $\times$ 3$^{2}$ = 28.26

Therefore, cross section of the cylinder = 28.26 cm$^{2}$

**Question 2: **Find the volume of the solid, whose base is bounded by the circle x$^{2}$ + y$^{2}$ = 25$^{2}$ and the cross sections perpendicular to the x-axis are squares.

** Solution: **
We know that, area of square, A = y$^{2}$

where, y is the length of the side

Given: x$^{2}$ + y$^{2}$ = 25$^{2}$

The formula to find the volume of the solid on the interval [a, b] is

V = $\int_{a}^{b}$ A(x) dx

V = $\int_{-5}^{5}$ y$^{2}$ dx

V = 2 $\int_{0}^{5}(625 - x^{2})$ dx

V = 2 [(625x - $\frac{x^{3}}{3}$)]$_{0}^{5}$

V = 2[3125 - 41.67]

V = 6166.66

Therefore, the volume of the solid is 6166.66 cubic units.