If a rectangular prism has a surface area of 198 square feet, a height of 6 feet and a lateral surface area of 144 square feet what is the base area of the prism? What is the volume of the prism?
length --- x
width ---- y
height ---- 6
volume = 6xy
The most common definition of lateral surface is the sum of all the surfaces of the object except the base.
So the sum of all six sides of our box is 198
the sum of the 5 sides , that is, excluding the base , is 144
so the area of the base = 196-144 = 52
but the area of the base is xy
so xy = 52
volume = 6xy = 6(52) = 312 ft^3
To find the base area of the rectangular prism, we first need to calculate the area of the lateral faces.
The lateral surface area is given as 144 square feet, which means that the sum of the areas of the four lateral faces is 144 square feet.
Since a rectangular prism has two pairs of congruent faces, the area of each lateral face is the same.
Therefore, the area of one lateral face is 144 square feet divided by 4, which is 36 square feet.
Since each lateral face is a rectangle, we can calculate the length and width of the base by dividing the area of the lateral face by the height of the prism.
The length of the base is obtained by dividing the area of one lateral face (36 square feet) by the height of the prism (6 feet), which is 6 square feet.
Similarly, the width of the base is also 6 square feet.
Therefore, the base area of the prism is the product of the length and width, which is 6 square feet multiplied by 6 square feet, equal to 36 square feet.
To find the volume of the prism, we multiply the base area by the height.
So, the volume is 36 square feet (the base area) multiplied by the height of 6 feet.
Therefore, the volume of the rectangular prism is 216 cubic feet.