Question

1. if the dimensions of the box below are doubled, by how many square centimeters does the surface area increase?

(image of a cube with side length 3 cm)
a. 8
b. 54
c. 162
d. 216

Explanation:

Step1: Find original surface area

A cube (since all sides are 3 cm) has surface area formula \( SA = 6s^2 \). For \( s = 3 \), \( SA_{original} = 6\times3^2 = 6\times9 = 54 \) \( cm^2 \).

Step2: Find new dimensions and surface area

Dimensions are doubled, so new side \( s_{new} = 3\times2 = 6 \) cm. New surface area \( SA_{new} = 6\times6^2 = 6\times36 = 216 \) \( cm^2 \).

Step3: Find the increase

Subtract original from new: \( 216 - 54 = 162 \) \( cm^2 \).

Answer:

C. 162