Quantitative Aptitude Ques 1026

Question: If the slant height of a right pyramid with square base is $ 4m $ and the total slant surface of the pyramid is $ 12m^{2}, $ then the ratio of total lateral surface and area of the base is

Options:

A) 16 : 3

B) 24 : 5

C) 32 : 9

D) 12 : 3

Show Answer

Answer:

Correct Answer: A

Solution:

  • $ \because $ Lateral surface area $ =\frac{1}{2}\times $ Perimeter of base $ \times $ Slant height

$ \Rightarrow $ $ 12=\frac{1}{2}\times Perimeterofbase\times 4 $

$ \Rightarrow $ Perimeter of base $ =\frac{12\times 2}{4}=6cm $

$ \therefore $ Side of square $ =\frac{6}{4}=\frac{3}{2}cm $ Now, area of base $ ={{(side)}^{2}}=\frac{9}{4}cm^{2} $

$ \therefore $ $ Ratio=\frac{12}{\frac{9}{4}}=\frac{4\times 4}{3}=16:3 $

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