Q6: Suppose your hair grows at the rate 1/32 in per day. What is the rate at which it grows in nanometers per second? [1 in = 2.54 cm, 1 d = 86 400 s, and 109 nm = 1 m] (a) 92.0 nm/s (b) 91.9 nm/s (c) 9.2 nm/s (d) 91.0 nm/s (e) 919.0 nm/s Q7: The JCR of a student hostel is 50.0 ft long and 26 ft wide and has 8.0-ft high ceilings. What is the volume of the interior of the room in cubic centimeters? [1 ft = 0.304 8 m]. (a) 2.94 × 103 cm3 (b) 3.17 × 103 cm3 (c) 2.94 × 108 cm3 (d) 2.9 × 108 cm3 (e) 2.98 × 108 cm3 4
Question
Q6: Suppose your hair grows at the rate 1/32 in per day. What is the rate at which it grows in nanometers per second? [1 in = 2.54 cm, 1 d = 86 400 s, and 109 nm = 1 m] (a) 92.0 nm/s (b) 91.9 nm/s (c) 9.2 nm/s (d) 91.0 nm/s (e) 919.0 nm/s Q7: The JCR of a student hostel is 50.0 ft long and 26 ft wide and has 8.0-ft high ceilings. What is the volume of the interior of the room in cubic centimeters? [1 ft = 0.304 8 m]. (a) 2.94 × 103 cm3 (b) 3.17 × 103 cm3 (c) 2.94 × 108 cm3 (d) 2.9 × 108 cm3 (e) 2.98 × 108 cm3 4
Solution
Sure, I can help with that. Let's solve these problems one by one.
Q6: First, we need to convert the rate from inches per day to nanometers per second.
1 inch/day = 1/32 inch/day = 0.03125 inch/day
Now, convert inches to centimeters:
0.03125 inch/day * 2.54 cm/inch = 0.079375 cm/day
Then, convert centimeters to meters:
0.079375 cm/day * 1 m/100 cm = 0.00079375 m/day
Next, convert meters to nanometers:
0.00079375 m/day * 10^9 nm/m = 793750000 nm/day
Finally, convert days to seconds:
793750000 nm/day * 1 day/86400 s = 919.0 nm/s
So, the answer is (e) 919.0 nm/s.
Q7: To find the volume of the room, we need to multiply its length, width, and height. But first, we need to convert the measurements from feet to centimeters.
Length = 50.0 ft * 0.3048 m/ft * 100 cm/m = 1524 cm Width = 26 ft * 0.3048 m/ft * 100 cm/m = 792.48 cm Height = 8.0 ft * 0.3048 m/ft * 100 cm/m = 243.84 cm
Volume = Length * Width * Height = 1524 cm * 792.48 cm * 243.84 cm = 2.94 × 10^8 cm^3
So, the answer is (c) 2.94 × 10^8 cm^3.
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