Question

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

Explanation:

Step1: Use the perimeter formula of a rectangle

The perimeter formula of a rectangle is \(P = 2(l + w)\), where \(P = 32\) and \(l=10\). Substitute into the formula: \(32=2(10 + w)\).

Step2: Solve for the width \(w\)

Divide both sides of \(32 = 2(10 + w)\) by \(2\): \(\frac{32}{2}=10 + w\), so \(16=10 + w\). Then subtract \(10\) from both sides: \(w=16 - 10=6\).
When a rectangle is rotated about a line parallel to one of its sides, the radius of the base of the resulting cylinder is equal to the length of the side perpendicular to the axis of rotation. Here, the width of the rectangle (since it is rotated about a line parallel to the length) is the radius of the base of the cylinder.

Answer:

6 units