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julia-pushkina [17]
3 years ago
14

“An architect is planning to incorporate several stone spheres of different sizes into the landscaping of a public park, and wor

kers 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
Mathematics
1 answer:
Artist 52 [7]3 years ago
6 0

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

C=2\pi r

<u><em>Find the radius of the sphere with a 5.50-meter circumference</em></u>

For C=5.50\ m

assume

\pi =3.14

substitute and solve for r

5.50=2(3.14)r

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

<u><em>Find the radius of the sphere with a 7.85-meter circumference</em></u>

For C=7.85\ m

assume

\pi =3.14

substitute and solve for r

7.85=2(3.14)r

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

step 2

Find the surface area of each sphere

The surface area of sphere is equal to

SA=4\pi r^{2}

<u><em>Find the surface area of sphere with a 5.50-meter circumference</em></u>

For r=0.88\ m

assume

\pi =3.14

substitute

SA=4(3.14)(0.88)^{2}

SA=9.73\ m^{2}

<u><em>Find the surface area of sphere with a 7.85-meter circumference</em></u>

For r=1.25\ m

assume

\pi =3.14

substitute

SA=4(3.14)(1.25)^{2}

SA=19.63\ m^{2}

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

<u><em>Find the cost of sphere with a 5.50-meter circumference</em></u>

9.73*(92)=\$895.16

therefore

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

<u><em>Find the cost of sphere with a 7.85-meter circumference</em></u>

19.63*(92)=\$1,805.96

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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