A regular square pyramid has side of its base 20 cm and height 45 cm is melted and recast into regular triangular pyramids of equilateral base of side 10 cm and height 10√3 cm. What are the total numbers of regular triangular pyramid?
Volume of regular square pyramid = 1/3 × (Area of base) × height
⇒ Volume of regular square pyramid = 1/3 × 400 × 45 = 6000 cm3
After melting and recasting, sum of volumes of ‘n’ regular triangular pyramids with equilateral base, volume of triangular pyramids would be equal to volume of regular square pyramid.
⇒ 6000 = n × 1/3 × (Area of equilateral triangular base of side 10 cm) × height
⇒ 6000 = n × 1/3 × (√3/4 × 100) × 10√3
⇒ n = 24
∴ Total numbers of regular triangular pyramid = 24