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

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