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,                \[a\times (ah)=40\times 4\] \[a\times 40=40\times 4\] \[a=4cm\]