Question 1
LEVEL 4
A statue with a volume of 3 m^3 is carved out of African Mahogany, which has a density of 50 kg/m^3.
Calculate the mass of this statue in kg.
Select the correct answer from the list below:
A: 150 kg
B: 17 kg
C: 0.06 kg
D: 53 kg
CORRECT ANSWER: A: 150 kg
WORKED SOLUTION:
Because we are looking for the mass, we need to cover the m in our density, mass, volume triangle.
This tells us that we need to multiply the density and the volume.
m=3\times50=150 kg
Question 2
LEVEL 4
The density of copper is 8.96 g/cm^3.
Calculate the volume of 26.88 g of copper in cm^3.
Select the correct answer from the list below:
A: 240.8448 cm^3
B: 0.33 cm^3
C: 3 cm^3
D: 35.84 cm^3
CORRECT ANSWER: C: 3 cm^3
WORKED SOLUTION:
Because we are looking for the volume, we need to cover the V in our density, mass, volume triangle.
This tells us that we need to divide the mass by the density.
V=26.88\div8.96=3 cm^3
Question 3
LEVEL 4
A carpenter plans to carve a doorstop out of a block of wood that has a density of 5 g/cm^3.
Calculate the mass of the doorstop, in g, if this is the design:
Select the correct answer from the list below:
A: 65 g
B: 150 g
C: 75 g
D: 3 g
CORRECT ANSWER: C: 75 g
WORKED SOLUTION:
First we need to work out the volume of the doorstop,
V = \dfrac{1}{2}\times5\times3\times2= 15 cm^3
Then to find the mass m,
m = 5 \times 15 = 75 g
Question 4
LEVEL 4
A cube has sides of length 20 cm and a mass of 5 kg. Find the density of this cube, in g/cm^3.
Select the correct answer from the list below:
A: 0.00625 g/cm^3
B: 250 g/cm^3
C: 62.5 g/cm^3
D: 0.625 g/cm^3
CORRECT ANSWER: D: 0.625 g/cm^3
WORKED SOLUTION:
Because we are looking for the density, we need to cover the d in our density, mass, volume triangle.
This tells us that we need to divide the mass by the volume. Before we can do this, we need to consider two points, the units and the volume.
Volume:
We don’t know the volume yet, but we can figure this out by the information we are given. We are told that the shape is a cube with sides of length 20 cm. We can find the volume of a cube by cubing its side lengths.
V=20^3=8000 cm^3
Units:
We are told to give the answer in g/cm^3, but our mass is in kg. We need to change this first.
m=5 kg =5000 g
And now that we have the correct volume and units, we just need to divide the mass by our volume to find the density.
d=\dfrac{5000}{8000} =0.625 g/cm^3
Question 5
LEVEL 4
An artist is creating an installation that involves a concrete sphere with a radius of 50 cm.
Given that density of concrete is 2400 g/m^3, calculate the mass of the sphere in kg.
You may use the formula V=\frac{4}{3}\pi r^3.
Select the correct answer from the list below:
A: 1260000000 kg
B: 1260 kg
C: 126 kg
D: 1.26 kg
CORRECT ANSWER: B: 1260 kg
WORKED SOLUTION:
Because we are looking for the mass, we need to cover the m in our density, mass, volume triangle.
This tells us that we need to multiply the density and the volume. Before we can do this, we need to consider two points, the units and the volume.
Units:
Because our answer will be in kg, we need to convert the g or kg so that they cancel later in our working. Because the 50 cm doesn’t have any powers on it, this will be the easiest one to change.
50 cm =0.5 m
Volume:
We don’t know the volume yet, but we can figure this out by the information we are given. We are told that the shape is a sphere with a radius of 0.5 m (after the conversion) and the formula V=\frac{4}{3}\pi r^3. All we need to do is put the radius in to find the volume.
V=\frac{4}{3}\pi \times(0.5)^3 =0.5236 m^3
And now, all we need to do is multiply our density and volume.
m=2400\times 0.5236=1260 kg (3sf)