Question

Arusha draws a rectangular prism that is made up of 2 connected cubes, each with side length e. The surface area of a certain rectangular prism with edge length e is represented by the formula SA = 10e (squared), and the volume of the prism is represented by the formula V = 2e (cubed).

A: What is the surface area of the prism if its edge length is 5 cm?
B: Arusha plans to build the prism and partially fill it with 150 cubic cm of sand. What fraction of the prism's volume will be filed by the sand?

Answer 1

The surface area of the prism with an edge length of 5 cm is 250
`cm^2`, and the fraction of the prism's volume filled by 150
`cm^3` of sand is 60%.

Step-by-step explanation:

To find the surface area of the prism with an edge length of 5 cm, we can substitute the given value into the formula for surface area: SA = 10e2. By substituting e = 5 cm, we get SA = 10 * 52 = 10 * 25 = 250 cm2. Therefore, the surface area of the prism is 250
`cm2`.

To find the fraction of the prism's volume that will be filled by the sand, we can use the formula for volume: V = 2e3. By substituting e = 5 cm, we get V = 2 * 53 = 2 * 125 = 250
`cm^3`. Since the sand will partially fill the prism with 150
`cm^3`. of sand, the fraction of the prism's volume filled by the sand is 150
`cm^3`. / 250 cm3 = 0.6 or 60%.

Answer 2

the surface area of the prism if the edge lenght is 5 centimeters would be 2500 because we already know that 10 is the lenght of the prism so if the width is 5 then what you would have to do is 10*5 which is 50 and then you would do 50 to the 2nd power which equals 2500 and that is your answer :)