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?
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.
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
To find out the cost of reseeding the lawn, we need to determine the area that Flash destroyed and then calculate the number of packages of grass seed needed. Let's break it down step-by-step:
Step 1: Calculate the area that Flash destroyed.
- The length of the leash is given as 10 ft, which means Flash can dig holes within a 10 ft radius around the pole.
- The area that Flash destroyed is equal to the area of a circle with a radius of 10 ft.
- The formula for the area of a circle is A = πr², where A is the area and r is the radius. The value of π is approximately 3.14.
- Substituting the values, we get A = 3.14 * (10 ft)².
- Evaluating the equation, we get A = 3.14 * 100 ft².
- So, the area that Flash destroyed is 314 ft².
Step 2: Calculate the number of packages of grass seed needed.
- Each package of grass seed covers 50 ft².
- To find the number of packages needed, we divide the area Flash destroyed by the coverage area of one package: 314 ft² / 50 ft².
- Performing the division, we get 6.28 (approximately).
- Since we cannot have a fraction of a package, Theo will need to buy 7 packages of grass seed.
Step 3: Calculate the cost of reseeding the lawn.
- Each package of grass seed costs $1.40.
- To find the total cost, we multiply the price per package by the number of packages: $1.40 * 7.
- Performing the multiplication, we get $9.80.
Therefore, it cost Theo $9.80 to reseed the lawn.
To find the cost for Theo to reseed the lawn, we first need to calculate the area of the lawn that Flash destroyed. We know that Flash was tied to a pole with a 10 ft. leash, so Flash was able to roam in a circular area around the pole.
The formula to find the area of a circle is A = πr^2, where A is the area and r is the radius. In this case, the radius is half the length of the leash, which is 10 ft / 2 = 5 ft.
Now we can calculate the area of the lawn that Flash destroyed:
A = πr^2 = π(5 ft)^2 = 25π ft^2.
Next, we need to convert this area to square feet, as that is the unit for the cost of grass seed. Since the cost is given per 50 square feet, we can divide the area by 50 to determine the number of packages of grass seed needed.
Number of packages = (25π ft^2) / (50 ft^2/package)
= (25π/50) packages
= (π/2) packages.
Now, we can calculate the cost of reseeding the lawn by multiplying the number of packages needed by the cost per package:
Cost = (π/2) packages * $1.40/package
= π/2 * $1.40
≈ $2.20.
Therefore, it cost Theo approximately $2.20 to reseed the lawn.