# GCSE Maths Help?

Thread starter 4 years ago
#1
An object will float in oil if its density is less than 0.7 g/cm^3
An object will float in water if its density is less than 1 g/cm^3

A spherical object has a radius of 0.38 meters.
Its mass is 200 kg.

Will the object float in oil or water?

Tick a box.

[ ] The object will float in oil and water.

[ ] The object will float in water but not in oil.

[ ] The object will not float in oil or water.

You must show your working out.

1000 kg/m^3 = 1 g/cm^3.

Volume of a sphere = 4/3 * pi * r^3.

[5 marks]
0
4 years ago
#2

The basic approach is to calculate the density of the object, from its mass divided by its volume (g/(cm)^3 is the most convenient here).
0
4 years ago
#3
So you can work out the density of the sphere:
mass/volume
There are two ways to do this now:
1) Use kg/(m^3) and then divide by 1000 as they tell you
2) Convert kg & m into g & cm, and then work out the answer
Now, compare the density with the two given facts and you should have an answer
Spoiler:
Show

Got B (Density 0.87g/cm^3)

0
4 years ago
#4
I got the density of the sphere as 0.870 (3sf) g/cm^3, which means that it will float in water but not in oil. Can't be asked to post my workings cause its too much writing lol
0
4 years ago
#5
To make it easier, convert the sphere's values to m and g

0.38 meters in cm = 38 cm
200kg in g = 200000g

Sphere volume
= 4/3 * pi * 38^3
= 219488/3 * pi

density = mass/volume
= 200000 / 219488/3 * pi
= 0.87... g/cm^3

The density is higher than 0.7 g/cm^3 so it will not float in oil but it is lower than 1 g/cm^3 so it will float in water.
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