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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

Haris
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AlanaCut
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  • Not following. You have $.113$ cm$^3$ of gold and each cube weighs 19.3 grams. Thus you have a total of $.113,\text {cm}^3\times 19.3,\frac {\text {grams}}{\text {cm}^3}=2.1809$ grams. – lulu Mar 08 '24 at 12:59
  • Here, following the units is the best way to get the answer (although maybe not the best way to understand). The $19.3$ figure has units of grams per cubic centimeter. The volume has units of cubic centimeters. You want grams. How do you get grams from the units $\frac{\text{grams}}{\text{cubic centimeters}}$ and $\text{cubic centimeter}$? You multiply, so the cubic centimeters "cancel." Your result is $2.18$ grams (not grams per cubic centimeter). – user469053 Mar 08 '24 at 12:59
  • Looking up "dimensional analysis" might lead you to more in-depth explanations and more example problems. – user469053 Mar 08 '24 at 13:01

1 Answers1

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The question says -

Each cm$^3$ of pure gold weighs $19.3$ grams.

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.

Haris
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