I need to find the surface area and volume of a right regular hexagonal prism. The height is 10cm and the sides of its base measure 18cm. You round to the nearest hundredth.
The prisms's hexagonal base area is six times the area of an equilateral triangle with side length 10 cm. Double that for the combined areas of top and bottom. There are also six rectangular sides, each with area 18 x 10 cm
To find the surface area and volume of a right regular hexagonal prism, we need to break down the problem into several steps.
Step 1: Find the area of one hexagon.
- Since the base of the prism is a regular hexagon, all of its sides are equal in length. The formula to find the area of a regular hexagon is A = (3√3/2) * s^2, where s is the length of the side.
- In this case, the length of the side (s) is 18cm.
- Plugging the values into the formula, we can calculate the area of one hexagon.
Step 2: Find the perimeter of the hexagon.
- The perimeter of a regular hexagon can be calculated by multiplying the length of one side by 6.
- In this case, the length of the side is also 18cm.
- Multiply 18cm by 6 to find the perimeter of the hexagon.
Step 3: Calculate the lateral surface area of the prism.
- The lateral surface area is the sum of the areas of the six rectangular faces of the prism.
- Since each rectangular face is the same as one of the hexagon's sides multiplied by the height of the prism, the formula for the lateral surface area is A = perimeter * height.
- Multiply the perimeter of the hexagon by the height of the prism to find the lateral surface area.
Step 4: Calculate the total surface area of the prism.
- The total surface area of a prism is the sum of the lateral surface area and the areas of the two bases.
- Since the bases are regular hexagons, we can use the formula from Step 1 to calculate the area of each base.
- Multiply the area of one hexagon by 2 to find the total area of the two bases.
- Add the lateral surface area to the total area of the two bases to get the total surface area of the prism.
Step 5: Calculate the volume of the prism.
- The volume of a prism can be calculated by multiplying the area of the base by the height.
- Multiply the area of one hexagon (from Step 1) by the height of the prism to find the volume.
Remember to round your answers to the nearest hundredth as specified.
Following these steps, you will be able to find the surface area and volume of the right regular hexagonal prism with a height of 10cm and sides of the base measuring 18cm.