Question

lesson 4: drilling for understanding

1. for the following diagrams, give the surface - area formula and label the dimensions needed to find the surface area on the diagram.

a.
sa=
b.
sa=
c.
sa=
d.
sa=

Explanation:

Step1: Identify surface - area formula for a rectangular prism

The surface - area of a rectangular prism with length $l$, width $w$, and height $h$ is given by $SA = 2(lw+lh + wh)$.

Step2: Identify surface - area formula for a cube

A cube has all sides equal. Let the side length be $s$. The surface - area formula is $SA=6s^{2}$.

Step3: Identify surface - area formula for a cylinder

For a cylinder with radius $r$ and height $h$, the surface - area formula is $SA = 2\pi r^{2}+2\pi rh$.

Step4: Identify surface - area formula for a square - based pyramid

For a square - based pyramid with base side length $s$ and slant height $l$, the surface - area formula is $SA=s^{2}+2sl$.

Answer:

a. $SA = 2(lw+lh + wh)$ (dimensions: length $l$, width $w$, height $h$)
b. $SA=6s^{2}$ (dimension: side length $s$)
c. $SA = 2\pi r^{2}+2\pi rh$ (dimensions: radius $r$, height $h$)
d. $SA=s^{2}+2sl$ (dimensions: base side length $s$, slant height $l$)