Question

A solid silver paperweight in the form of a square pyramid is shown below. If silver costs $0.12 per cubic centimeter, how much would it cost to manufacture six paperweights?

Answer 1

Answer:

The cost of 6 silver paper weight is $0.24  b² h

Step-by-step explanation:

Given as :

The cost of silver paper weight = $0.12 per cubic centimeter

A solid silver paperweight in the form of a square pyramid

Let The base of square pyramid = b cm

The height of square pyramid = h cm

Now, The volume of square pyramid is given as :

Volume = $\frac{1}{3}$ × base² × height

Or, v = $\frac{1}{3}$ × b² × h

So , The volume of square pyramid =  $\frac{1}{3}$ b² h  cm³

Now, The cost of 1 cm³ silver paperweight = $0.12

So, The cost of  $\frac{1}{3}$ b² h cm³ = $0.12 × $\frac{1}{3}$ b²h

I.e The cost of  $\frac{1}{3}$ b² h cm³ =  $\frac{0.12}{3}$ b² h

∴ The cost of  $\frac{1}{3}$ b² h cm³ = $0.04 b² h

So, The cost of  6 paper weight = $0.04 b² h × 6

I.e The cost of  6 paper weight = $0.24 b² h

Hence The cost of 6 silver paper weight is $0.24  b² h  . Answer