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dlcrzngl
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Tyro
Asked: 2021-05-06T08:14:56+00:00 In: ,

Find the radius and volume of a cylinder

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A cylinder has a height of 10 and a surface
area of 78π. Find the radius and volume of this
cylinder.

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1 Answer

  2. acedstud

    First, let us assume that the cylinder is closed at both ends, then the total surface area of the cylinder is given by S=2\pi r^2+2\pi rh, where r and h are the radius and the height of the cylinder respectively.

    Given that the surface area is 78\pi and the height is 10, we have

    78\pi=2\pi r^2+2\pi r(10)=2\pi(r^2+10r)

    Dividing both sides by 2, we have

    39=r^2+10r\Rightarrow r^2+10r-39=0\Rightarrow(r-3)(r+13)=0\Rightarrow r-3=0 or r+13=0\Rightarrow r=3 or r=-13, but radius cannot be negative, so r=3.

    Therefore, the radius is 3.

     

    The volume of a cylinder is given by V=\pi r^2h=\pi(3)^2(10)=90\pi.

    Therefore, the volume of the cylinder is 90\pi.

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