Question

creating three - dimensional solids. rectangle abcd has a perimeter of 32 units and will be rotated about line k. what is the three - dimensional solid created? what is the radius of a base? 3 units 6 units 10 units 12 units

Explanation:

Step1: Recall rotation - solid concept

When a rectangle is rotated about one of its sides, a cylinder is formed.

Step2: Find the other side of the rectangle

Let the length of the rectangle be $l = 10$ and the width be $w$. The perimeter of a rectangle is $P=2(l + w)$. Given $P = 32$, so $32=2(10 + w)$. Solving for $w$:
First, divide both sides of the equation by 2: $\frac{32}{2}=10 + w$, which gives $16=10 + w$. Then subtract 10 from both sides: $w=16 - 10=6$.

Step3: Determine the radius of the base of the cylinder

When the rectangle is rotated about the line $k$ (which is along the length of 10), the width of the rectangle becomes the radius of the base of the cylinder. So the radius $r = 6$ units.

Answer:

What is the three - dimensional solid created? Cylinder
What is the radius of a base? 6 units