Question

4.6 surface area of prisms and cylinders
an art student must paint and decorate a small wooden box. the width of the box is 2 cm, the height is 3 cm, and the length of the box is 5 cm. what is the surface area that the student will paint?
cm squared

Explanation:

Step1: Recall surface - area formula for a rectangular prism

The formula for the surface area $S$ of a rectangular prism is $S = 2(lw+lh + wh)$, where $l$ is the length, $w$ is the width, and $h$ is the height.

Step2: Substitute the given values

Given $l = 5$ cm, $w = 2$ cm, and $h = 3$ cm. First, calculate $lw$, $lh$, and $wh$:
$lw=5\times2 = 10$ cm², $lh = 5\times3=15$ cm², $wh=2\times3 = 6$ cm².

Step3: Calculate the sum inside the parentheses

$lw+lh + wh=10 + 15+6=31$ cm².

Step4: Multiply by 2

$S = 2\times31=62$ cm².

Answer:

62