Question

he specific gravity of gold is 19.3. Write a MATLAB program that will ask the user to input the mass of a cube of solid gold in units of kilograms and display the length of a single side of the cube in units of inches. The output should display a sentence like the following one, with the length formatted to two decimal places.

Answer 1

Explanation:

Specific gravity of gold = G = 19.3

We know that the specific gravity of gold is given by

G = ρg/ρw

Where ρg is the density of gold and ρw is density of water which is 1000 kg/m³

Now we can find out the density of gold

ρg = G*ρw

ρg = 19.3*1000

ρg = 19300 kg/m³

We also know that density and mass are related as

density = mass/volume

ρg = m/V

where volume of cube is given by

V = s³

Where s is the length of each side

ρg = m/s³

s³ = m/ρg

s = ∛(m/ρg) meters

To convert from meters to inches multiply by 39.37

s = ∛(m/ρg)*39.37 inches

Finally we get the relation of mass and length of side of a gold cube.

Matlab Code:

density = 19300;

% get input from the user that is mass of gold in kg

mass= input('Please input mass of gold in kg\n');

% check if the user has entered valid mass if it is less than or equal to zero then display error

if (mass<=0)

fprintf('Error: Wrong input! please try again');

else

% If the mass is valid then calculate the length of side of the cube

s = (mass/density);

% nthroot() is used to calculate the cube root

s = nthroot(s,3);

% to convert from meters to inches

s = s*39.37;

% finally display the length with 2 decimal points accuracy

fprintf('The length of side of the gold cube is: %.2f inches\n', s);

end

Output:

Please input mass of gold in kg

-2

Error: Wrong input! please try again

Please input mass of gold in kg

0.4

The length of side of the gold cube is: 1.08 inches