Question

what box will travel the furthest?
a box l
b box p
c box m

box | mass (g) | volume (cm³)
l | 3 | 3
m | 7 | 9
n | 14 | 64
o | 18 | 140
p | 22 | 125

Explanation:

Step1: Calculate density for each box

Density formula: $
ho = \frac{m}{V}$ (mass over volume).

• Box L: $

ho_L = \frac{3}{3} = 1$ g/cm³

• Box M: $

ho_M = \frac{7}{9} \approx 0.78$ g/cm³

• Box N: $

ho_N = \frac{14}{64} \approx 0.22$ g/cm³

• Box O: $

ho_O = \frac{18}{140} \approx 0.13$ g/cm³

• Box P: $

ho_P = \frac{22}{125} = 0.176$ g/cm³

Step2: Relate density to travel distance

Objects with lower density (lighter for same volume, or larger volume for same mass) travel farther (assuming same ramp/force). Box O has the lowest density (≈0.13) among them? Wait, no—wait Box N: 14/64≈0.22, Box O:18/140≈0.13, Box P:22/125=0.176. Wait, recalculate Box O: 18 divided by 140 is 0.12857, Box N:14/64=0.21875, Box M:7/9≈0.777, Box L:1, Box P:22/125=0.176. Wait, Box O has lower density? Wait no, wait the question is which box travels farthest. Lower density means less mass per volume, so lighter, so travels farther. Wait Box O: mass 18g, volume 140cm³: density ~0.13. Box P:22g, 125cm³: ~0.176. Box N:14g,64cm³: ~0.218. Box M:7g,9cm³: ~0.777. Box L:3g,3cm³:1. So Box O has lowest density? Wait but wait the table: Box L: mass 3, volume 3; M:7,9; N:14,64; O:18,140; P:22,125. Wait, maybe I mixed up. Wait, no—wait, maybe it's about buoyancy or rolling, but in a ramp, lower density (lighter) moves farther. Wait, but wait Box O: volume 140 is large, mass 18 is small. So Box O is lightest per volume. Wait, but let's check again. Wait, maybe I made a mistake. Wait Box O: 18g, 140cm³: density 0.128. Box P:22g,125cm³: 0.176. Box N:14g,64cm³:0.218. So Box O has the lowest density. Wait, but the options: A is Box L, B is Box P, C is Box M? Wait no, the options are A:Box L, B:Box P, C:Box M? Wait no, the left options: A:Box L, B:Box P, C:Box M? Wait no, the image shows options A: Box L, B: Box P, C: Box M? Wait no, the user's image: options A: Box L, B: Box P, C: Box M? Wait, no, the original problem: "What box will travel the furthest? A. Box L, B. Box P, C. Box M". Wait, no, my calculation was wrong. Wait, maybe I mixed up mass and volume. Wait, maybe it's mass over volume, but actually, for objects rolling down, the one with less mass (or lower density) travels farther. Wait, Box O is not an option? Wait the options are A:Box L, B:Box P, C:Box M? Wait the user's options: A. Box L, B. Box P, C. Box M. Wait, my mistake: the boxes in the table are L, M, N, O, P. But the options are A:Box L, B:Box P, C:Box M. Wait, so we need to check L, M, P. Wait Box L: density 1, M:7/9≈0.78, P:22/125=0.176. Wait, Box P has lower density than M and L. Wait, but the options: B is Box P. Wait, maybe I messed up the options. Wait the user's options: A. Box L, B. Box P, C. Box M. So among L, P, M: Box P has density 22/125=0.176, M:7/9≈0.78, L:1. So Box P is lighter (lower density) than M and L, so travels farther. Wait, but earlier I thought O was lower, but O is not an option. So the options are L, P, M. So Box P (option B) has lower density than L and M, so travels farthest.

Answer:

B. Box P