Question

1. a)  Why is the following situation impossible? A student's dormitory room measures 3.0 m by 3.3 m, and its ceiling is 3.7 m high. After the student completes his physics course, he displays his dedication by completely wallpapering the walls of the room with the pages from his physics textbook which has 960 pages of text on 480, 0.21 m × 0.28 m sheets. He even covers the door and window.

b) A section of land has an area of 1 square mile and contains 640 acres. Determine the number of square meters in 4 acres.

_____ m^2

c) Suppose the U.S. national debt is about $18 trillion. If payments were made at the rate of $2,000 per second, how many years would it take to pay off the debt, assuming no interest were charged? Note: Before doing these calculations, try to guess at the answers. You may be very surprised.
_____ yr

Answer 1

a)
Consider L, B abd H be the length, breadth and Height of the dormitory room
SA = 2 [LB + BH + LH]
= 2 x [3 x 3.3 + 3.3 x 3.7 + 3 x 3.7]
= 66.42 m²

Area of a 960 text book pages = 480 x [0.21 x 0.28]
= 28.224 m²

So, one textbook is not enough to cover even half of the room.

b)
1 square miles = 640 acres
1 acre = 1/640 square miles
4 acres = 4/640 square miles
= 1/160 square miles

1 mile = 1609.34 m
1 square mile = (1609.34)² m²
= 2589975.2356 m²

4 acres = 1/160 square miles = 1/160 [2589975.2356] m²
= 16187.35 m²

c)
Total debt = $18 trillion
= $18 x 10¹²

Amount paid per second = $2000
Total time taken to pay $18 trillion = [$18 x 10¹²] / [$2000]
= 9 x 10⁹ s

Number of years = [9 x 10⁹] / [365 x 24 x 60 x 60]
= 285.39 years