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isaiahromero15
03.01.2020 •
Mathematics
An architect is planning several stone spheres of different sizes into the landscaping of a public park, and workers who will be applying the finish to the exterior of the spheres need to know the surface area of each sphere. the finishing process costs $92 per square meter. the surface area of a sphere is equal to 4(pi)r2 where r is the radius of the sphere.
how much would it cost to finish a sphere with a 5.50-meter circumference and a 7.85-meter circumference?
a) $900
b) $1200
c) $1800
d) $2800
e) $3200
f) $4500
Solved
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Ответ:
the answer is closest to option d) $2800
Step-by-step explanation:
Assume,
Cost per square meter = y = 92$
Step 1:
For Sphere 1:
Circumference = C1 = 5.5 m
Formula for Circumference is;
C = 6.2832(R)
Where R = radius of sphere
Therefore for radius;
C1 = 6.2832(R1)
5.5 = 6.2832(R1)
R1 = 5.5/6.2832
R1 = 0.87 m
Formula for Area;
A1 = 4π(R1)²
Since,
π = 3.14
Therefore;
A1 = 4*3.14*(0.87)²
A1 = 9.51 m²
Cost of finishing for sphere 1 will be;
X1 = 92*A1
X1 = 92*9.51
X1 = $875
Step 2:
For Sphere 2:
Circumference = C2 = 7.85 m
Formula for Circumference is;
C = 6.2832(R)
Where R = radius of sphere
Therefore for radius;
C2 = 6.2832(R2)
7.85 = 6.2832(R2)
R2 = 7.85/6.2832
R2 = 1.25 m
Formula for Area;
A1 = 4π(R2)²
Since,
π = 3.14
Therefore;
A1 = 4*3.14*(1.25)²
A1 = 19.63 m²
Cost of finishing for sphere 1 will be;
X2 = 92*A2
X2 = 92*19.63
X2 = $1,806
Step 3:
Now for total cost;
X = X1 + X2
X = 875 + 1806
X = $2,681
Ответ: