Question

A toy pyramid (not shown) is made from poly (methyl methacrylate), better known by its trade term Lucite. The toy pyramid has a regular hexagonal base of $15{cm}^2$ and a height of $4cm$. There is a semispherical indentation of diameter $2cm$ at the base of the pyramid. If the weight of the pyramid is $21.129g$, then find the density of Lucite. (Density equals mass divided by volume.)

• A. $1.06g/{cm}^3$
• B. $0.365g/{cm}^3$
• C. $2.09g/{cm}^3$
• D. $6.51g/{cm}^3$

Answer 1

The correct option is B $0.365g/{cm}^3$

Volume of the pyramid $=$ area of the hexagonal base $\times$ height of the pyramid

$\therefore$ volume $=15\times 4=60cc$

Semi Spherical indentation at the base, will have volume $=$ $\frac{2}{3}\times \pi r^3$

$=\frac{2}{3}\times \pi \times 1=2.095cc$

The actual volume thus becomes $60-2.095=57.905cc$

Density $=$ mass/volume $=\frac{21.129}{57.905}=0.365g/cc$