the square shown has a perimeter of 32 units. the square is rotated about line k. what shape is created by…

the square shown has a perimeter of 32 units. the square 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

the square shown has a perimeter of 32 units. the square 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

Explanation:

Step1: Find side - length of the square

The perimeter of a square is $P = 4s$, where $s$ is the side - length. Given $P = 32$ units, then $4s=32$, so $s=\frac{32}{4}=8$ units.

Step2: Determine the shape and base - radius

When a square is rotated about a line parallel to one of its sides, a cylinder is formed. The radius of the base of the cylinder is equal to the side - length of the square, so $r = 8$ units.

Step3: Calculate the circumference of the base

Using the formula $C = 2\pi r$, with $r = 8$ units, we have $C=2\pi\times8=16\pi\approx16\times 3.14 = 50.24\approx50$ units.

Answer:

a cylinder with a circumference of about 50 units