I am trying to solve a question from Leaving Cert. Ordinary Level Maths 2018 Paper 2.
A solid sphere is made of gold.
It has a volume of $0.113$cm$^3$.
Each cm$^3$ of pure gold weighs $19.3$ grams.
I am trying to find the number of grams of pure gold in the sphere.
The marking scheme says I am to multiply $0.113$cm$^3$ by $19.3$ grams, but I don't understand why.
The answer is "$2.18$". I am assuming this is $2.18$ grams / cm$^3$.
Does this mean that there are $2.18$ grams of gold per cm$^3$ of the sphere?
Any feedback would be greatly appreciated.
Thanks,
Alana
The question says -
This is just another way of saying that the sphere's gold content is $19.3$ g / cm$^3$.
The question wants you to find the mass of pure gold in the sphere ($0.113$ cm$^3$) in grams. So you multiply the mass per unit volume ($19.3$ g / cm$^3$) and the volume ($0.113$ cm$^3$) together. Your answer would be
$$\frac{19.3 \text{ g}}{\text{cm}^3} \times 0.113 \text{ cm}^3 \approx 2.18 \text{ g}$$
As you can see the two instances of "cm$^3$" cancel out and we are left with grams only.