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24 May, 00:16

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

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Answers (1)
  1. 24 May, 01:01
    0
    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
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