Question

Theo tied his dog, Flash, to a pole in the middle of the yard using a 10 ft. leash. Flash dug holes in the yard everywhere he could reach.
Theo had to reseed the part of the lawn that Flash destroyed.
Grass seed costs $1.40 per package and covers 50 square feet.
What did it cost Theo to reseed the lawn?

Answer 1

What you have here is a circle. The center is the pole and the radius is the length of the rope. The area of this circle is what Theo needs to reseed.
Area of a circle = pi r^2 (pi r squared)
r = 10ft
pi = 3.14
Area to be reseeded = pi(10)^2 = pi(100) = 314 ft^2
Each bag of grass seed will cover 50 ft^2, so Theo will need:
314ft^2/50ft^2 = 6.28 bags of seed
Since you can't buy partial bags of seed, Theo will need 7 bags of grass seed.
The cost of 7 bags of grass seed:
7 x $1.40 = $9.80
So, it cost Theo $9.80 to reseed the lawn.

Answer 2

The area of a circle is πr² and in this case r=10.
So the destroyed lawn area is: π(10)² ≈ 314.16 square feet.
It will take: 314.16÷50= 6.283 packages of seed to repair it.
Since he can't buy a fraction of a package, we'll round up to 7.
The 7 packages of seed will cos:t 7×1.40= $9.80