Respuesta :
Answer:
Area of sidewalk = [tex]346.5 ft^2[/tex]
Bags of concrete = 277
Step-by-step explanation:
The diameter of the circular fountain is 28 ft. Radius = 28 / 2 = 14 ft
The thickness of the sidewalk is 3.5 ft. This means they want to add 3.5 ft to each radius of the fountain.
To find the area of the sidewalk alone, we have to find the area of the sidewalk alone and then subtract it from the area of the sidewalk and fountain.
That is:
[tex]A_s = A_{s+f} - A_f[/tex]
The fountain is circular and its radius is 14 ft. Hence, its area will be:
[tex]A_f = \pi r^2[/tex]
[tex]A_f = \pi *14^2 = 616 ft^2[/tex]
The sidewalk and fountain together also form a circular shape. Their joint radius will be:
R = 14 + 3.5 = 17.5 ft
Hence, the area will be:
[tex]A_{s + f} = \pi R^2 \\A_{s + f} = \pi * 17.5 * 17.5 = 962.5 ft^2[/tex]
Hence, the area of the sidewalk alone will be:
[tex]A_s = 962.5 - 616 = 346.5 ft^2[/tex]
This is the area of the sidewalk.
For every square foot ([tex]ft^2[/tex]), 0.8 bag of concrete will be used. This means that for [tex]346.5 ft^2[/tex]:
Bags of concrete = 0.8 * 346.5 = 277.2 ≅ 277
At least 277 bags of concrete will be used for the new sidewalk.
A) The area of the sidewalk rounded to the tenths place is; 346.4 ft²
B) The minimum number of bags of concrete needed is; 278 bags
We are given;
Diameter of circular fountain; D = 28 ft
Radius of circular fountain; R = D/2 = 28/2 = 14
Width of side walk; x = 3.5 ft
Formula for area of a circle is;
A = πr²
Area of circular fountain with side walk;
A = π(14 + 3.5)²
A = 306.25π
Area of circular fountain without side walk;
a = π(14)²
a = 196π
Thus;
Area of side walk = 306.25π - 196π
Area of side walk = 346.360 ft²
approximation to the nearest tenth = 346.4 ft²
We are told that 0.8 bags of concrete will be required for every square foot. Thus;
Minimum number of bags required = 0.8 × 346.4
Minimum number of bags required ≈ 278 bags
Read more about area of a circle at; https://brainly.com/question/15673093
