Question

Matt plans to give Phoebe a gift for her 15th birthday. He wants the gift item to be placed in a cubical box whose volume is 192 cm^3. How much wrapping paper is needed to wrap the whole surface of the box?

a. 96 cm^2
b. 384 cm^2
c. 768 cm^2
d. 1536 cm^2

Answer 1

To calculate the amount of wrapping paper needed for a cubical box with a volume of 192 cm³, one must first calculate the side length of the cube and then calculate the total surface area. However, the answer from the calculation does not match any of the given options, indicating a potential error in the question or the options.

Step-by-step explanation:

To find out how much wrapping paper is needed to wrap the cubical box, we first need to calculate the side length of the cube, given the volume. The volume V of a cube is given by V = a3, where a is the side length of the cube. We have V = 192 cm3:

a3 = 192 cm3
a = ∓(192 cm3)
a = 5.848 cm (approximately)

We know the surface area A of a cube is given by A = 6a2, so substituting the side length we get:

A = 6(5.848 cm)2
A = 6(34.2 cm2) (approximately)
A = 205.2 cm2 (approximately)

Since the surface area turns out not to be an exact match with any of the provided options, we can conclude that there may have been a miscalculation or a typo in the original problem or options. We would need to choose the option closest to our calculation, but any selection would be an assumption.