Scaling Dimensions

Mathematical Equivalence

ON

When you ​ (a)   the dimensions of a rectangular prism, the ​ (b)   increases by a factor of 4. This is because the surface area is proportional to ​ (c)   of the dimensions. If the original box requires 2 ounces of paint, the new box will need ​ (d)   ounces of paint.

• surface area

• the square

• double

The volume of the box, which determines how much ​ (a)   it can hold. The original box holds ​ (b)   of sugar. With ​ (c)   dimensions, the new box will hold ​ ​ (d)     cups of sugar. This demonstrates how changes in dimensions affect both surface area and ​ (e)   , with volume increasing more significantly.

• volume

• sugar

• 15 cups

• doubled

In the figure above, a dilation from A to A' has occurred. What is the scale factor?

Mathematical Equivalence

ON

Kiran probably multiplied the volume by the ​ (a)   . He needs to ​ (b)   by the ​ (c)   of the scale factor.

​ (d)   times 10 = ​ (e)   cubic inches

• scale factor

• cube

• 3.5 cubed

• 428.75

• multiply

• original area

• the square of the scale factor of the sides

• 8

• original area

• the square of the scale factor of the sides

• 6

• dilation affects area

• square of that factor

Find the volume of the similar pyramids.

• 12 in³

• 21.3 ft³

• 16 ft³

• 6.75 in³