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A cylinder has a radius of 4 inches and a height of 5 inches. If the radius of the cylinder is tripled and the height remains the same to create a new cylinder, what will be the difference in the surface areas of the two cylinders? Answer in terms of Pi.

Respuesta :

mhanifa

Answer:

  • 336π in²

Step-by-step explanation:

Cylinder 1

  • r₁= 4 in
  • h = 5 in

Cylinder 2

  • r₂ = 3*4 = 12 in
  • h = 5 in

Surface area of cylinders:

  • S = 2πr(r + h)
  • S₁ = 2π*4*(4 + 5) = 72π in²
  • S₂ = 2π*12*(12 + 5) = 408π in²

The difference is:

  • S₂ - S₁ =
  • 408π - 72π =
  • 336π in²
TheCutePrincess

Question:-

A cylinder has a radius of 4 inches and a height of 5 inches. If the radius of the cylinder is tripled and the height remains the same to create a new cylinder, what will be the difference in the surface areas of the two cylinders ? Answer in terms of Pi.

Answer:-

Given:-

A cylinder has a radius of 4 inches and a height of 5 inches.

To Find:-

If the radius of the cylinder is tripled and the height remains the same to create a new cylinder, what will be the difference in the surface areas of the two cylinders ?

Solution:-

Let in case of 1st cylinder,

[tex] \bullet [/tex] Radius [tex] (r_1) [/tex] is 4 inches

[tex] \bullet [/tex] Height is 5 inches

And in case of 2nd cylinder,

[tex] \bullet [/tex] Radius [tex] (r_2) [/tex] is 3 × 4 = 12 inches [as in the question it is given that the radius of the cylinder is tripled]

[tex] \bullet [/tex] Height is 5 inches

Now,

Surface area [tex] (s_1) [/tex] of 1st cylinder

is 2πr(r + h) = 2π × 4(4 + 5)

= 8π(9)

= 72π sq inches

Surface area [tex] (s_2) [/tex] of 2nd cylinder

is 2πr(r + h) = 2π × 12(12 + 5)

= 24π(17)

= 408π sq inches

[tex] \therefore [/tex] The difference in the surface areas of the two cylinders is = [tex] (s_2 \: - \: s_1) [/tex] = (408π - 72π) = 336π sq inches

The difference in the surface areas of the two cylinders is 336π sq inches. [Answer]

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