Question
A garden is being created in an area shaped like an isosceles trapezoid, as shown Topsoil is needed to fill the garden, to a depth of 2 ft, Each bag of topsoil has 16 cubic feet of soil. How many bags will be needed to fill the garden?
Answers
GPT 3.5
To find the volume of the garden, we first need to find the area of the base of the trapezoid.
The formula for the area of a trapezoid is A = (1/2) * (a + b) * h, where a and b are the lengths of the two bases and h is the height.
In this case:
a = 10 ft (top base)
b = 15 ft (bottom base)
h = 8 ft (height)
A = (1/2) * (10 + 15) * 8
A = (1/2) * 25 * 8
A = (1/2) * 200
A = 100 square feet
Now, to find the volume of the garden, we multiply the area of the base by the depth:
V = 100 * 2
V = 200 cubic feet
Since each bag has 16 cubic feet of soil, we divide the total volume by the volume of each bag to find the number of bags needed:
Number of bags = 200 / 16
Number of bags = 12.5
Since we can't have a fraction of a bag, we will need to round up to the nearest whole number. Therefore, 13 bags will be needed to fill the garden.
The formula for the area of a trapezoid is A = (1/2) * (a + b) * h, where a and b are the lengths of the two bases and h is the height.
In this case:
a = 10 ft (top base)
b = 15 ft (bottom base)
h = 8 ft (height)
A = (1/2) * (10 + 15) * 8
A = (1/2) * 25 * 8
A = (1/2) * 200
A = 100 square feet
Now, to find the volume of the garden, we multiply the area of the base by the depth:
V = 100 * 2
V = 200 cubic feet
Since each bag has 16 cubic feet of soil, we divide the total volume by the volume of each bag to find the number of bags needed:
Number of bags = 200 / 16
Number of bags = 12.5
Since we can't have a fraction of a bag, we will need to round up to the nearest whole number. Therefore, 13 bags will be needed to fill the garden.