question_answer

If the slant height of a right pyramid with square base is 4 m and the total slant surface of the pyramid is 12 sq m, then the ratio of total slant surface and area of the base is

A)  12 : 3  

B)  16 : 3

C)  24 : 5  

D)  32 : 9

Correct Answer: B

Solution :

Given, total slant surface area =12m2 Slant height = 4 m Now, area of one slant side of prism \[=\frac{12}{4}=3\,\,{{m}^{2}}\] \[\Rightarrow \]\[\frac{1}{2}\times 4\times a=3\,\,\,\,\,\,\,\,\Rightarrow a=\frac{3}{2}\,\,m\] Now, area of base\[={{\text{(Side)}}^{2}}={{\left( \frac{3}{2} \right)}^{2}}=\left( \frac{9}{4} \right)\,\,{{m}^{2}}\] \[\therefore \]Required ratio\[=\frac{12}{9/4}=\frac{12\times 4}{9}=\frac{16}{3}=16:3\]