Q63. - Algebra 1

Question

Choose a geometric formula and explain how the order of operations applies when using the formula.

Step-by-Step Solution

Answer

The geometric formula for the total surface area of a cylinder with radius r and height h is $2\pi rh+2\pi r^2$.

Step 1 –Choosing a geometric shape

Let’s choose a cylindrical geometric shape. Its total surface area is the sum of the curved surface of the cylinder and the area of the top and bottom circular surfaces.

Step 2 – Example of applying operations when using formula

The expression $b(c-d)-e$ can be written as

$\begin{array}{l}b(c-d)÷e=\left[\right(b\times c)-(b\times d\left)\right]÷e\\ =(bc-bd)÷e\\ =\frac{(bc-bd)}{e}\end{array}$

Step 3 - DESCRIPTION OF STEP

It is known that the area of a circle is $\pi r^2$. A cylinder has a circular top and a circular bottom. Let the radius of the cylinder be r. Then the total surface area of the two circular regions is $(\pi r^2+\pi r^2)=2\pi r^2$.

Again, it is further known that the curved surface area of a cylinder with radius r and height h is given by $2\pi rh$.

Thus, the total surface area of the cylinder is the sum of the curved surface area and the area of the two circular regions which is $2\pi rh+2\pi r^2$.

Hence, the geometric formula for the total surface area of a cylinder with radius r and height h is $2\pi rh+2\pi r^2$.