Find the total surface area and volume of the solid object shown to the right.
(Round to three significant digits.)
8.47 radius 16.2 height
To find the surface area of the solid object, we need to find the area of the curved surface (lateral area) and the area of the two circular bases.
The curved surface area (lateral area) can be found using the formula for the lateral surface area of a cylinder:
Lateral Area = 2 * π * radius * height
Substituting the given values:
Lateral Area = 2 * 3.1416 * 8.47 * 16.2
= 860.4081 square units
The area of each circular base can be found using the formula for the area of a circle:
Base Area = π * radius^2
Substituting the given radius:
Base Area = 3.1416 * 8.47^2
= 225.7640 square units
The total surface area is the sum of the lateral area and the area of the two circular bases:
Total Surface Area = Lateral Area + 2 * Base Area
= 860.4081 + 2 * 225.7640
= 1311.9361 square units
To find the volume of the solid object, we use the formula for the volume of a cylinder:
Volume = π * radius^2 * height
Substituting the given values:
Volume = 3.1416 * 8.47^2 * 16.2
= 3626.7432 cubic units
Therefore, the total surface area of the solid object is approximately 1311.9361 square units and the volume is approximately 3626.7432 cubic units.