Pyramid. In the adjoining solid, a square based pyramid is
situated on the top of a square based cuboid so that
the total height of the solid is 15 cm. If the volume
of the pyramid and cuboid are 300 cm and 600 cm
respectively, find the height of the pyramid.
15 cm
adean of the same
The heich

9 cm.

Step-by-step explanation:

Let the height of the pyramid be h cm, then the height of the cuboid is (15 - h) cm.

Volume of the pyramid:

= 1/3 * h * s^2      where s is the length of a side of the square base.

= hs^2/3 cm^3

Volume of the cuboid:

= s^2(15 - h).

So we have:

hs^2/ 3 = 300(1)

s^2(15 - h) = 600(2)

From  equation (1) :

h s^2 = 900

s^2 = 900/h

Now substitute for s^2 in  equation (2) :

(900/h)(15 - h) = 600

Multiply through by h:

900(15 - h) = 600h

13500 - 900h = 600h

1500h = 13500

h = 9 cm (answer).

step-by-step explanation: