Ask Question

Suppose the length and width of the box in exercise 12 double. Does the surface area S double? Explain

10cm 24cm and 27cm are the lengths in exercise 12

+3
Answers (1)
  1. 9 July, 01:19
    0
    No, it does not.

    In general, surface area is the sum of the areas of each face of a prism. In a rectangular prism, we have length, width, and height.

    The area of the bottom of the prism and the top of the prism is the same, and can be represented as l*w. This means that together, it is 2lw.

    The area of the left and right faces of the prism is the same, and can be represented as l*h. This means that together, it is 2lh.

    The area of the front and back faces of the prism is the same, and can be represented as w*h. This means that together, it is 2wh.

    This gives us the equation

    SA = 2lw+2lh+2wh

    If we double the length and width, making them each 2l, we then have:

    SA = 2 (2l*2w) + 2 (2l*h) + 2 (2w*h)

    = 2 (4lw) + 4lh + 4wh

    = 8lw + 4lh + 4wh

    If the surface area had been doubled, we would expect

    4lw + 4lh + 4wh

    No, it is not doubled.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “Suppose the length and width of the box in exercise 12 double. Does the surface area S double? Explain 10cm 24cm and 27cm are the lengths ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers