Scale Factor Volume Surface Area

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?

Mathematical Equivalence

ON

When multiplying a length by a scale factor, does the scale factor change? ​ When adjusting the surface area of a solid, the scale factor must be ​ . When adjusting the volume of a solid, the scale factor must be​ .

• No

• squared

• cubed

• Yes

• Not relevant

• left alone

It takes 2 ounces of paint to completely cover all 6 sides of a rectangular prism box which holds 15 cups of sugar. Double the dimensions of the box. Approximately how much paint would the new box need?

• 8

• 16

• 4

• 3

If the height of the rectangular prism is multiplied by a scale factor of 4, which of the following is true?

• The volume remains the same.

• The volume is eight times as large.

• The volume is also multiplied by a scale factor of 4.

• The volume increases by 4.

Kaitlyn has a rectangular prism that has the same dimensions as the one shown except for the height 4 times as tall. What is true about the volume of Kaitlyn's rectangular prism?

• Her prism's volume is 4 cubic centimeters less than the volume of the prism above.

• Her prism's volume is 4 cubic centimeters more than the volume of the prism above.

• Her prism's volume is 4 times the volume of the prism above.

If the length of a prism with length = 10 m, width = 5 m and width = 2 m, is doubled, which of the following is true about its volume?

• The new volume is 3 times the old.

• The new volume is 1/2 the old.

• The new volume is 2 times the old.

• The new volume is 4 times the old.

The volume of a rectangular prism is 250 m³. If the height is multiplied by a scale factor of 1/2, what is the new volume?

• 250 m³

• 500 m³

• 125 m³

• 75 m³

If the length of a rectangular prism is changed by a factor of 3, which of the following is true?

• The surface area changes by a factor of 3.

• The volume changes by a factor of 3.

• The surface area changes by 3.

• The volume changes by 3.

The volume of a rectangular solid is 960 cubic inches. The dimensions of the base are 12 inches by 10 inches. What is the height of the solid?

• 8 inches

• 80 inches

• 9.6 inches

• 10 inches

Carl's rectangular swimming pool has a volume of 600 cubic feet. The neighbor's pool has the same length and height, but the width is three times larger. What is the volume of the neighbor's pool?

• 1800 cubic feet

• 1200 cubic feet

• 900 cubic feet

• 600 cubic feet