All edges of a Square Pyramid are 18cm.what is it's volume?
Answers
Answer:
In this problem, we are not given h. But h is essential to calculate volume. So we will find it first.
1. Imagine ⊿OCB inside the pyramid. See fig.33.18.b above
• It should satisfy the following conditions:
♦ OCB must be right angled
♦ O must coincide with the centre of the base
♦ C must coincide with a corner the base square
♦ B must coincide with the apex
• We will get:
♦ OB = height of pyramid
♦ OC = half of a diagonal of the base
♦ BC = Lateral edge = 18 cm
2. Applying Pythagoras theorem, we get:
OB = √[BC2 - OC2] = √[182 - OC2]
3. Now OC = half of the diagonal
• Full diagonal = √[182 + 182] = 18√2 cm. See fig.33.18.c
• So half diagonal = OC = 9√2
4. Substituting this value of OC in (2), we get:
• OB = √[182 - (9√2)2] = √[324-(81×2)] = √[162] cm
5. Then volume = 1⁄3 × (a2h) = 1⁄3 × 182 × √162 = 1⁄3 × 182 × √[9×9×2] = 972√2 cm3 .