Question

consider the figure shown. indicate whether each statement is correct or incorrect. when the rectangle is rotated about one of its longer sides, a cylinder of base radius 4 units and height 7 units is formed select choice when the rectangle is rotated about one of its longer sides, a cylinder of base radius 3.5 units and height 4 units is formed select choice

Explanation:

Step1: Recall cylinder - formation concept

When a rectangle is rotated about one of its sides, the side about which it is rotated becomes the height of the cylinder and the other - side becomes the radius of the base of the cylinder.

Step2: Analyze the first statement

The rectangle has sides 4 and 7. When rotated about the longer side (7 units), the shorter side (4 units) becomes the radius of the base of the cylinder and the longer side (7 units) becomes the height of the cylinder. So, a cylinder of base radius 4 units and height 7 units is formed. This statement is correct.

Step3: Analyze the second statement

When rotated about the longer side (7 units), the radius of the base should be 4 units (the shorter side of the rectangle) and the height should be 7 units. A cylinder of base radius 3.5 units and height 4 units is not formed. This statement is incorrect.

Answer:

First statement: Correct
Second statement: Incorrect