Question

Two similar prisms have heights 4 cm and 10cm what is the ratio of their surface areas

Answer 1

Let k be the scale factor relating two similar prisms $P_{1}$ and $P_{2}$, such that for corresponding parts of prisms $P_{1}$ and $P_{2}$ (for heights, in particular) we have $k= \frac{height\ of \ P_{1} }{height \ of\ P_{2} }$. In our case $k= \frac{4}{10} = \frac{2}{5}$.
For surfaces area we have $\frac{Surface \ area \ of \ P_{1} }{Surface \ area \ of \ P_{2}} = k^{2} =( \frac{2}{5} )^{2}= \frac{4}{25}$.
So, the right answer is 4:25 (choice B)