Question

One polyhedron has surface ares 4,400 cm² and volume 16,000 cm³. Give the surtace ares and the volume of the polphedron's image for a siation with the given scale factor: scale factor = ½

surface area = _________cm²
volume = ______ cm³

Answer 1

To find the surface area and volume of the image of a polyhedron, multiply the scale factor with the surface area and volume of the original polyhedron. The surface area of the image is 2,200 cm² and the volume is 8,000 cm³.

Step-by-step explanation:

To find the surface area and volume of the image of the polyhedron, we need to multiply the given scale factor with the surface area and volume of the original polyhedron. Let's say the scale factor is k. Since the surface area of the original polyhedron is 4,400 cm² and the volume is 16,000 cm³:

The surface area of the image will be k * 4,400 cm² and the volume of the image will be k * 16,000 cm³. Substituting the given scale factor of ½:

The surface area of the image = ½ * 4,400 cm² = 2,200 cm²

The volume of the image = ½ * 16,000 cm³ = 8,000 cm³