A sphere has a surface area of 160 square centimeters. Which choice is the closest to its diameter? Use 3.14 to approximate pi.

Question

I have been working on this math question for almost 2 hours already and i think now i need someone to help me with this.

Answer 1

Hello! To figure out this problem you will want to use two relationships:

 

• The surface area of a sphere: A=4(pi)(r²) , where A is surface area and r is the radius, and we are estimating pi at 3.14
• Diameter = 2 x radius

 

With these facts we can solve the problem:

1. A=160               <------this we know from the problem
2. 160=4(3.14)(r²) <------now we apply the surface area formula
3. 160=12.56r²         <------multiply 4*3.14
4. r²=160/12.56     <------divide both sides by 12.56
5. r=√(160/12.56) <------square root both sides
6. since diameter=2 x radius, and we have the radius in #5, diameter = 2(√(160/12.56)) = 7.138cm

Answer 2

SA_sphere = 4∏r²

 

Everything is constant save the radius, so we just need to solve for it by isolating r:

160 cm² = 4 * 3.14r²

40 cm²= 3.14r²

12.7388 cm² = r²

We take the square root of both sides, and:

3.5691 cm = r

 

d_iameter = 2r

d = 3.5691 cm * 2

d = 7.1382 cm

 

Answer 3

Surface Area of a Sphere = 4(Pi)(r^2)

 

Therefore 160=4(3.14)(r^2)

 

                 40 = (3.14)(r^2)

 

              12.74 = r^2

   

              3.57 = r, Diameter = 2(r), so d=7.14

Answer 4

The surface area a sphere is

 

A = 4πr²  ,  where  r = d/2

 

 

A = 4π(d/2)²

 

A = 4π(d² / 4)

 

A = πd²

 

d = √(A / π)

 

Substitute the values into this formula to obtain your diameter.