XAT 2017 — QA & DI Question 12
PyramidEasy
The Volume of a pyramid with a square base is 200 cubic cm. 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?
Answer & solution
- A
12 cm
- B
13 cm
14 cm
- D
15 cm
- E
16 cm
Solution
Let the side of the square base AB = BC = CD = DA = ‘a’.
Height OB = 13.
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Volume of a square base pyramid = a2 × h/3 = 200 cm3
⇒ a2 = 600/13
Diagonal AC = a√2
⇒ AB = a/√2
In right âOAB, AO2 = AB2 + OB2
⇒ AO2 = (a/√2)2 + 132
⇒ AO2 = a2/2 + 169
⇒ AO2 = 300/13 + 169 = 2497/13
⇒ AO ≈ 13.86
Thus, the length of the slant slope (when rounded to the nearest integer) = 14 cm
Hence, option (c).