Dilation of Solids

A food company is designing boxes for several products. Each box is a rectangular prism. The company makes a single serving cereal box that contains 1.2 ounces of cereal. They plan to make an extra large box for school cafeterias. The extra large box will be a dilation of the single serving box using a scale factor of 4. How many ounces of cereal will the extra large box contain? Explain or show your reasoning.

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HSG-GMD

HSN-Q.A.1

A food company is designing boxes for several products. Each box is a rectangular prism. The company also wants to offer a family size box of cereal. The family size box will be a dilation of the single serving 1.2-ounce box. It must contain 18.75 ounces of cereal. What scale factor does the company need to use for the family size box? Explain or show your reasoning.

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HSG-GMD

HSN-Q.A.1

A food company is designing boxes for several products. Each box is a rectangular prism. The food company is now designing soup boxes. The largest box of soup will be a dilation of the smallest box using a scale factor of 2. The smallest box must hold 8 fluid ounces or about 15 cubic inches of soup. Find a set of dimensions for the largest box. Round your answers to the nearest tenth if necessary. Explain or show your reasoning.

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HSG-GMD

HSN-Q.A.1

A trapezoid has an area of 100 square units. What scale factor would be required to dilate the trapezoid to have each area?

• 6400 square units

• 900 square units

• 100 square units

• 25 square units

The scale factor for this dilation is:

Mathematical Equivalence

ON

A triangle has an area of 6 square inches and a perimeter of 12 inches. Suppose it is dilated by some scale factor, and the area and perimeter of the image are calculated. Match each graph with the relationship it represents.

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Select all solids whose cross sections are dilations of some two-dimensional shape using a point directly above the shape as a center and scale factors ranging from 0 to 1.

• cylinder

• cube

• triangular prism

• cone

• triangular pyramid

• 3

• 9

• There are 9 copies of ABCD within A'B'C'D. The original ABCD is the first one. There are 7 full congruent copies of ABCD. Figures P and Q together make an additional copy for total of 9.

• 3

• 9

• There are 9 copies of ABCD within A'B'C'D. The original ABCD is the first one. There are 7 full congruent copies of ABCD. Figures P and Q together make an additional copy for total of 9.

• 3

• 9

• There are 9 copies of ABCD within A'B'C'D. The original ABCD is the first one. There are 7 full congruent copies of ABCD. Figures P and Q together make an additional copy for total of 9.