A 3 kg pine board is 20 cm wide, 2 cm thick, and 2 m long. What is the density of the board?

Question

A. 240 kg/m3
B. 267 kg/m3
C. 469 kg/m3
D. 375 kg/m3

Answer 1

Density = Mass / Volume

We're given the Mass as 3 kg.

To calculate the volume you consider the shape of the board. It's a RECTANGULAR SOLID. We're given the dimensions of the board:
L = 2 m
W = 20 cm
H = 2 cm (thickness)

V = L x W x H

Before you can just "plug in & crunch the numbers" you must convert any units in order to "make them the same". It doesn't matter what units you choose. We'll calculate using CENTIMETERS.

Converting L: 2m x (100cm/m) = 200 cm

Calculating Volume: V = L x W x H:
V = (200 cm)(20 cm)(2 cm) = 8000 cm^3

The answer is experssed in kg / m^3 so we convert:
V = (8000 cm^3)(1m / 100cm)^3 = 0.008 m^3

Density = Mass / Volume = 3 kg / 0.008 m^3
Density = 375 kg / m^3