Question

The square shown has a perimeter of 32 units. The square is rotated about line k.

A square with a perimeter of 32 units is rotated about line k.

What shape is created by the rotation and what is the approximate circumference of the base?

Circumference of a circle: C = 2πr

a cone with a base circumference of about 25 units
a cone with a base circumference of about 50 units
a cylinder with a circumference of about 25 units
a cylinder with a circumference of about 50 units

Answer 1

A cylinder with a circumference of about 50 units is formed.

Step-by-step explanation:

Step 1:

The perimeter of the square is 32 units. The perimeter of a square is given by 4 times its side length.

$(4) sidelength = 32, sidelength = \frac{32}{4} = 8.$

So the side length of the square is 8 units.

If a square is rotated a cylinder will be formed. So the options with a cone are wrong as a cone is formed when a triangle is rotated.

Step 2:

To calculate the circumference of the cylinder, we multiply 2π with the radius. The radius is the same as the side length of the square. So r is 8 units.

The circumference of the cylinder $= 2\pi r = (2) (3.1415)(8) = 50.264.$

So the circumference of the cylinder is approximately equal to 50 units so the answer is the fourth option, a cylinder with a circumference of about 50 units.

Answer 2

A cylinder with a circumference of about 50 units is formed.

Step-by-step explanation:

Step 1:

The perimeter of the square is 32 units. The perimeter of a square is given by 4 times its side length.

So the side length of the square is 8 units.

If a square is rotated a cylinder will be formed. So the options with a cone are wrong as a cone is formed when a triangle is rotated.

Step 2:

To calculate the circumference of the cylinder, we multiply 2π with the radius. The radius is the same as the side length of the square. So r is 8 units.

The circumference of the cylinder

So the circumference of the cylinder is approximately equal to 50 units so the answer is the fourth option, a cylinder with a circumference of about 50 units.

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