Question

Which expressions show the volume and the surface area of this cube-shaped packing box?

A) V = (114)^3 ft³, SA = 6 * (114)^2 ft²
B) V = (114)^3 ft³, SA = 3 * (114)^2 ft²
C) V = 6 * (114)^3 ft³, SA = (114)^2 ft²
D) V = 3 * (114)^3 ft³, SA = 6 * (114)^2 ft²

Answer 1

A) V = (114)^3 ft³, SA = 6 * (114)^2 ft²

Explanation:

For a cube-shaped packing box, the volume (V) of a cube is calculated by cubing the length of one side, while the surface area (SA) is found by multiplying the area of one face by the number of faces. In this case, the side length of the cube is 114 feet.

The volume of a cube is given by V = a^3, where a is the length of one side. Therefore, the volume V is 114 cubed, expressed as (114)^3 ft³.

The surface area of a cube is SA = 6a^2, where a is the length of one side. Substituting the value of a as 114, the surface area SA is 6 * (114)^2 ft². This accounts for the six faces of the cube, each having an area of (114)^2 square feet.

Hence, option A correctly represents the volume and surface area of the cube-shaped packing box, with the volume V as (114)^3 ft³ and the surface area SA as 6 * (114)^2 ft², in accordance with the formulas for a cube's volume and surface area.

Answer 2

The volume and surface area of the cube-shaped packing box can be calculated as follows:

V = (114)³ ft³ SA = 6 * (114)² ft²

Step-by-step explanation:

To find the volume of the cube-shaped packing box, we need to cube the length of the box, which is 114 feet. Therefore, the volume of the box is:

V = 114 x 114 x 114 = (114)³ ft³

To find the surface area of the box, we need to multiply the length of the box by the width of the box, which is also 114 feet. Therefore, the surface area of the box is:

SA = 114 x 114 = 1296 ft²

However, we need to double the surface area to account for both the top and bottom surfaces of the box, since each surface has the same area. Therefore, the final surface area of the box is:

SA = 2 x 1296 = 2592 ft²