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“An architect is planning to incorporate several stone spheres of different sizes into the landscaping of a public park, and workers who will be applying a 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 4πr2, where r is the radius of the sphere.“In the table, select the value that is closest to the cost of finishing a sphere with a 5.50-meter circumference as well as the cost of finishing a sphere with a 7.85-meter circumference. Make only two selections, one in each column.”Circumference 5.50 m Circumference 7.85 m Finishing cost$900$1,200$1,800$2,800$3,200$4,500

Respuesta :

calculista

Answer:

Part 1) The value that is closest to the cost of finishing a sphere with a 5.50-meter circumference is $900

Part 2) The value that is closest to the cost of finishing a sphere with a 7.85-meter circumference is $1,800

Step-by-step explanation:

Step 1

Find the radius of each sphere

we know that

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

Find the radius of the sphere with a 5.50-meter circumference

For [tex]C=5.50\ m[/tex]

assume

[tex]\pi =3.14[/tex]

substitute and solve for r

[tex]5.50=2(3.14)r[/tex]

[tex]r=5.50/[2(3.14)]=0.88\ m[/tex]

Find the radius of the sphere with a 7.85-meter circumference

For [tex]C=7.85\ m[/tex]

assume

[tex]\pi =3.14[/tex]

substitute and solve for r

[tex]7.85=2(3.14)r[/tex]

[tex]r=7.85/[2(3.14)]=1.25\ m[/tex]

step 2

Find the surface area of each sphere

The surface area of sphere is equal to

[tex]SA=4\pi r^{2}[/tex]

Find the surface area of sphere with a 5.50-meter circumference

For [tex]r=0.88\ m[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]SA=4(3.14)(0.88)^{2}[/tex]

[tex]SA=9.73\ m^{2}[/tex]

Find the surface area of sphere with a 7.85-meter circumference

For [tex]r=1.25\ m[/tex]

assume

[tex]\pi =3.14[/tex]

substitute

[tex]SA=4(3.14)(1.25)^{2}[/tex]

[tex]SA=19.63\ m^{2}[/tex]

step 3

Find the cost of finishing each sphere

we know that

To find out the cost , multiply the surface area by $92 per square meter

Find the cost of sphere with a 5.50-meter circumference

[tex]9.73*(92)=\$895.16[/tex]

therefore

The value that is closest to the cost of finishing a sphere with a 5.50-meter circumference is $900

Find the cost of sphere with a 7.85-meter circumference

[tex]19.63*(92)=\$1,805.96[/tex]

therefore

The value that is closest to the cost of finishing a sphere with a 7.85-meter circumference is $1,800

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