Width-16 inches Length-10 inches
Height- 2 inches

Describe the shape of the cross section when the box is cut parallel to the base.

What is the surface area of the box?

What is the surface area of the box if it is scaled up by a factor of 10?

What is the volume of the box?

What is the volume of the box if it is scaled down by a factor of 1/10?

rectangle

424 in.²

42,400 in.²

320 in.³

0.32 in.³

Step-by-step 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.

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