Big Ideas Math: Modeling Real Life, Grade 8
BI
Big Ideas Math: Modeling Real Life, Grade 8 View details
Chapter Review
Continue to next subchapter

Exercise 21 Page 457

When two solids are similar, the ratio of their surface areas is equal to the ratio of their corresponding linear measures squared.

86.6yd^2

Practice makes perfect

We know the height of two rectangular prisms that are similar, but the surface area of just one of them.

For two similar solids, the ratio of their surface areas is equal to the ratio of their corresponding linear measures squared. Surface area of the smaller solid/Surface area of the bigger solid = (Height of the smaller solid/Height of the bigger solid)^2 We know that the bigger solid has a height of 8 yards and a surface area of 154 square yards. We also know that the height of the smaller solid is 6 yards. We can substitute these values into the formula and calculate the surface area of the smaller solid S.

Surface area of the smaller solid/Surface area of the bigger solid=(Height of the smaller solid/Height of the bigger solid)^2
S/154=(6/8)^2
â–¼
Solve for S
S/154=6^2/8^2
S/154=36/64
S=5544/64
S=86.625
S≈86.6

The surface area of the smaller rectangular prism is approximately 86.6 square yards.