Question

The volume of pyramid A is the volume of pyramid B. If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B is the volume of pyramid A.

Answer 1

Given :

Two pyramid with same volume .

To Find :

If the height of pyramid B increases to twice that of pyramid A, the new volume of pyramid B .

Solution :

$V_a=V_b$

Volume of pyramid is given by :

$V=\dfrac{\text{Area of base}\times height}{3}\\\\V=\dfrac{Ah}{3}$

Now , h'=3h

$V'_b=\dfrac{Ah'}{3}\\\\V'_b=3\dfrac{Ah}{3}\\\\V'_b=3V_a$

Therefore , new volume of pyramid B is 3 times the value of pyramid A .

Hence , this is the required solution .