Answer:
rectangle
424 in.²
42,400 in.²
320 in.³
0.32 in.³
Explanation:
The box has the shape of a rectangular prism.
The cross section of the box is a rectangle.
The length and width are the length and width of the base of the prism.
surface area = perimeter of base × height + 2 × length × width
surface area = 2(length + width) × height + 2 × length × width
surface area = 2(10 in. + 16 in.) × 2 in. + 2 × 10 in. × 16 in.
surface area = 104 in.² + 320 in.²
surface area = 424 in.²
When you scale a solid by a factor of k on a linear measurement, the area is scaled by a factor of k². Since the linear dimensions are scaled by a factor of 10, then the surface area is scaled by a factor os 10² = 100. The surface area of the box scaled by a factor of 10 is 424 in.² × 100 = 42,400 in.²
volume = length × width × height
volume = 10 in. × 16 in. × 2 in.
volume = 320 in.³
When you scale the linear dimensions of a solid by a factor of k, the volume is scaled by a factor of k³. The linear scale factor is 1/10. The change in volume is a factor of (1/10)³ = 1/1000. The original volume is 320 in.³. The scaled volume is 320 in.³ × 1/1000 = 0.32 in.³.