Rectangle rect is rotated 360° about the y-axis.

what is the resulting solid of revolution? provide any key dimensions.
what is the surface area of the resulting solid of revolution? state the formula to be used, show all of your work, and use appropriate units in your answer.
what is the volume of the resulting solid of revolution? state the formula to be used, show all of your work, and use appropriate units in your answer.

The surface area = 120π units² ≅ 377 units²

The volume of the cylinder = 144π ≅ 452.4 units³

Step-by-step explanation:

* When a rectangle is rotating around one of the axis, 360°

 then, the formed figure is a cylinder withe height equal the

 side which rotated over it and the radius is the other dimension

∵ RECT is rotated 360° about the y-axis

∴ It formed a cylinder with height = RE and radius = EC

- R = (0 , 3 , 6) , E = (0 , 7 , 6) , C = (0 , 3 , 0) , T = (0 , 7 , 0)

∴ The length of RE = 7 - 3 = 4 units ⇒ height of the cylinder

∴ The length of EC = 6 - 0 = 6 units ⇒ radius of the cylinder

* The surface area of the cylinder = lateral area + 2 × area of the base

∵ Lateral area = perimeter of the base × height

∵ The base is a circle with radius = 6 units

∴ The perimeter of the base = 2πr = 2π(6) = 12π units

∵ The length of the height is 4 units

∴ The lateral area = 12π × 4 = 48π units²

∴ The area of the base = πr² = π(6²) = 36π units²

∴ The surface area = 48π + 2 × 36π = 120π units² ≅ 377 units²

* The formula of the volume of the cylinder is area of the base × height

∵ Area of the base = 36π units²

∵ The height = 4 units

∴ The volume of the cylinder = 36π × 4 = 144π ≅ 452.4 units³

arrange the equations with like terms in columns.

analyze the coefficients of x or y.

add the equations and solve for the remaining variable.

substitute the value into either equation and solve.

check the solution.

step-by-step explanation: