Question

part a — formula recall (fill in the blanks)

1. surface area of a cylinder: sa = ____ + ____
2. volume of a cone: v = ________________________
3. surface area of a rectangular prism: sa =

________________________

1. volume of a sphere: v = ________________________
2. surface area of a pyramid: sa = ________________________

Explanation:

Step1: Surface Area of a cylinder

A cylinder has two circular bases and a lateral surface. The area of each base is $\pi r^{2}$ (where $r$ is the radius of the base) and the lateral surface area is $2\pi rh$ (where $h$ is the height of the cylinder). So, $SA = 2\pi r^{2}+2\pi rh$.

Step2: Volume of a cone

The volume formula for a cone is derived from the volume of a cylinder. The volume of a cylinder is $V=\pi r^{2}h$. A cone has one - third of the volume of a cylinder with the same base radius $r$ and height $h$. So, $V=\frac{1}{3}\pi r^{2}h$.

Step3: Surface Area of a rectangular prism

A rectangular prism has 6 faces. Let the length be $l$, the width be $w$, and the height be $h$. The pairs of opposite faces have areas $lw$, $lh$, and $wh$. So, $SA = 2lw + 2lh+2wh$.

Step4: Volume of a sphere

The volume formula for a sphere is $V=\frac{4}{3}\pi r^{3}$ (where $r$ is the radius of the sphere).

Step5: Surface Area of a pyramid

A pyramid has a base with area $B$ and triangular lateral faces. The sum of the areas of the lateral faces is called the lateral surface area $LSA$. So, $SA=B + LSA$.

Answer:

1. $2\pi r^{2}+2\pi rh$
2. $\frac{1}{3}\pi r^{2}h$
3. $2lw + 2lh + 2wh$
4. $\frac{4}{3}\pi r^{3}$
5. $B+LSA$