Navajo Sand

1 prealgebra word problem?

The Navajo and Pueblo Indians create large, circular sand paintings as part of the traditional healing ceremonies. How much more area does a sand painting with a 20-foot diameter have compared with one with a 5-foot diameter?

306.5 ft²
184.9 ft²
236.0 ft²
294.4 ft²

Formula needed: Area = πr²

We need to compare the area of a 20-ft diameter circle with one with a 5-ft diameter.

Given: 20-ft diameter circle
Means: radius = 10 ft since diameter = 2*radius

Given: 5-ft diameter circle
Means: radius = 2.5 ft since diameter = 2*radius

Larger Area = π(10 ft)² = 100π square feet = 314.159265 square feet

Smaller Area = π(2.5 ft)² = 6.25π square feet = 19.6349541 square feet

Difference in Area = Larger Area - Smaller Area
Difference in Area = 314.159265 ft^2 - 19.6349541 ft^2
Difference in Area = 294.524311 square feet

The closest choice is 294.4 ft^2.

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