Sign in to view assessments and invite other educators
Sign in using your existing Kendall Hunt account. If you don’t have one, create an educator account.
Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.
If your teacher gives you the problem card:
Read the data card, and discuss your reasoning.
If your teacher gives you the data card:
Suppose a solid is dilated. If we know the factor by which the surface area or volume scale changed, we can work backward to find the scale factor of dilation. Then we can use that information to solve problems.
A company sells 10 inch by 10 inch by 14 inch 5-gallon aquariums, but a museum wants to buy a 135-gallon aquarium with the same shape. The company needs to know the dimensions of the new tank and by what factor the surface area will change.
Gallons are a measure of volume. So, the volume of the tank increases by a factor of . To find the scale factor for the dimensions of the tank, calculate the cube root of 27, or 3. This tells us that the height, length, and width of the tank will each be multiplied by 3. Next, we can square the scale factor of 3 to find that the tank’s surface area will increase by a factor of 32 = 9.
|
original aquarium |
dilated aquarium |
|
|---|---|---|
| height (inches) | 10 | |
| length (inches) | 14 | |
| width (inches) | 10 | |
| surface area (square inches) | 760 | |
| volume (gallons) | 5 |