SSC
Quantitative Aptitude
Mensuration
Question Bank
Mensuration-II (II)
question_answer
The base of a right prism is an equilateral triangle. If the lateral surface area and volume is \[120\,c{{m}^{2}},\] \[40\sqrt{3}\,c{{m}^{3}}\]respectively, then the side of base of the prism is [SSC CGL Tier II, 2014]
A)4 cm
B)5 cm
C)7 cm
D)40 cm
Correct Answer:
A
Solution :
[a] Lateral surface area of a prism = 120 ah + ah + ah =120 3 ah = 120 \[ah=\frac{120}{3}\] ah = 40 ...(i) Volume of prism \[=40\times \sqrt{3}\] \[=40\times \sqrt{3}\] \[{{a}^{2}}h=40\times 4\] (ii) From Eq. (i) ah = 40 Then, \[a\times (ah)=40\times 4\] \[a\times 40=40\times 4\] \[a=4cm\]