Question

The radius of the cross-section of an inflated cycle tyre is 7 cm. The distance of the centre of the cross section from the axis is 20 cm. Find the volume of air in the tyre.

Answer 1

We know that area is something that is occupied by an object when it is resting on a surface i.e area is the space which is used by the object. Whereas cross-sectional area is an area which we obtain when the same object is cut into two pieces. The simplest (and most commonly used) area calculations are for squares and rectangles. To find the area of a rectangle, multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.

Complete step by step answer
We know that the cross-sectional area is the area of a two-dimensional shape that is obtained when a three-dimensional object - such as a cylinder - is sliced perpendicular to some specified axis at a point. For example, the cross-section of a cylinder - when sliced parallel to its base is a circle.
For example, a cuboid is a rectangular prism. The ends of a cuboid are rectangular and it has identical rectangular cross-sections when cut by a plane parallel to the ends. Prisms are named according to the shape of their base (or cross-section).
Volume = area of cross section $\times$ length Here, Area of the cross section $=\pi r^{2}$ $=22/7\times 7\times 7$
$=154 \mathrm{sq} \mathrm{cm}$
Length is nothing but the circumference of the center part = $2 \pi r$ $=2\times 22/7\times 20$
$=880 / 7 \mathrm{cm}$
Now,

**The required volume of the tyre = Area of the cross section $\times$ Length $=154\times 880/7$
$=19360c{{m}^{3}}$ **

Note: We know that area is measured in "square" units. The area of a figure is the number of squares required to cover it completely, like tiles on a floor. Area of a square = side times side. Since each side of a square is the same, it can simply be the length of one side squared. Surface area is the sum of the areas of all the faces of the solid figure. Finding the surface area of a solid figure is like finding how much wrapping paper that is required to cover the solid; it is the area of the outside faces of a box. Volume is the amount of space inside of the solid figure.