nuttynathan101
Answered

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The lateral surface area of cone A is exactly 1/2 the lateral surface area of
cylinder B.

OA. True
OB. False

The Lateral Surface Area Of Cone A Is Exactly 12 The Lateral Surface Area Of Cylinder B OA True OB False class=

Sagot :

sqdancefan

Answer:

  B.  False

Step-by-step explanation:

You want to compare the lateral surface areas of a cone and cylinder, where the slant height of the cone is twice the height of the cylinder. Your proposition is that the cone's lateral area is half that of the cylinder.

Cone lateral area

Effectively, the lateral area of a cone is the area of a triangle whose base is the circumference of the cone, and whose height is the cone's slant height. The formula for the lateral area of a cone of radius r and slant-height s is ...

  A = πrs

For the given dimensions (s=2h), the lateral area is ...

  A = πr(2h) = 2πrh

Cylinder lateral area

The lateral area of a cylinder is the area of a rectangle whose base is the circumference of the cylinder, and whose height is the cylinder's height. The formula for the lateral area of a cylinder of radius r and height h is ...

  A = 2πrh

Comparison

The lateral areas of the given figures are both 2πrh, so one is not half the other.

The proposition is False.

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