the area of rectangle abde is 270 square inches. the rectangle is rotated about a line that passes through…

the area of rectangle abde is 270 square inches. the rectangle is rotated about a line that passes through points c and f. which best describes the resulting three - dimensional shape? a rectangular prism with an edge length of 9 inches a rectangular prism with an edge length of 18 inches a cylinder with a base radius of 9 inches a cylinder with a base radius of 18 inches

the area of rectangle abde is 270 square inches. the rectangle is rotated about a line that passes through points c and f. which best describes the resulting three - dimensional shape? a rectangular prism with an edge length of 9 inches a rectangular prism with an edge length of 18 inches a cylinder with a base radius of 9 inches a cylinder with a base radius of 18 inches

Answer

Answer:

C. a cylinder with a base radius of 9 inches

Explanation:

Step1: Find the other side - length of rectangle

Given area (A = 270) square - inches and one side (AB=15) inches. Using (A = l\times w), if (l = 15) inches, then (w=\frac{A}{l}=\frac{270}{15}=18) inches.

Step2: Analyze the rotation

When rectangle (ABDE) is rotated about the line through (C) and (F), the resulting three - dimensional shape is a cylinder. The distance from the axis of rotation (line (CF)) to the edge of the rectangle is half of the length of the side perpendicular to (AB). Since the side perpendicular to (AB) has length 18 inches, the radius of the base of the resulting cylinder is (\frac{18}{2}=9) inches.