Xavier Aptitude Test 2017 Paper

Question : 51 of 97

Marks: +1, -0

The volume of a pyramid with a square base is 200 cm

^{3}

. The height of the pyramid is 13 cm. What will be the length of the slant edges (i.e. the distance between the apex and any other vertex), rounded to the nearest integer?

12 cm
13 cm
14 cm
15 cm
16 cm

Validate

Solution:

(c)

Volume of fyramid =

\ {1}/{3} \×

area of base

\×

height

\⇒{1}/{3} \× a^{2} \× h=200

⇒ a^{2}=\ {200 \× 3}{13}=\ {600}/{13}

Also, Area of square (base)

=a^{2}= {1}/{2} d^{2}

\⇒ d^{2}=2 × a^{2}=\ {1200}/{13}

⇒\ {d}=\√{\ {1200}/{13}} ⇒{\ {d}}/{2}=\√{ {1}/{4} ×{1200}/{13}}=\√{\ {300}/{13}}

Thus, required length of slant edge

=\√{13^{2}+ {\ {d}^{2}}/{4}}=\ √{169+ {300}/{13}}=\√{\ {2497}/{13}} ≅√{192} \≅ 14 \ {cm}

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