Question

A king wanted to gift something to his queen. So, he ordered the goldsmiths to make the following shape out of pure gold.
The surface area of the shape is $200{\text{cm}}^2$ and the thickness is $10\text{cm}$. Find:

1. The volume of gold required to make the shape.
2. If density of pure gold is $19.3{\text{g cm}}^{-3}$, find the amount of gold needed to make the shape in kg.
3. If gold costs $\text{Rs.}5000/-$ per gram, find the total cost of making the shape.

Answer 1

1. The volume of gold required to make the shape = surface area of the shape $\times$ thickness of the shape

Given,
Area of the top surface = $200{\text{cm}}^2$
Thickness of the shape = $10\text{cm}$
$\text{v}=200\times 10=2000{\text{cm}}^3$

$\therefore$ volume of gold required = $2000{\text{cm}}^3$

2. Mass of the shape = density of the shape $\times$ volume of the shape.
Given,
density of gold = $19.3{\text{g cm}}^{-3}$

mass, $\text{m}=19.3\times 2000=38,600\text{g}=38.6\text{kg}$

3. Cost of making the shape = mass of the shape $\times$ cost of gold per gram
cost of gold per gram = $\text{Rs.}5000/-$

cost of making the shape = $5,000\times 38,600=\text{Rs.}19,30,00,000/-$

So, the king had to spent $19.3$ crores of rupees to make the gift to his queen.