Question

1) A triangular pyramid has a base area of 72cm squared and a height/altitude of 9 cm. If a cross section is cut 3 cm from the base of the pyramid, find the area of the cross section.2) Find the volume of the entire pyramid.

Answer 1

Given data:

Base area of square = 72cm

Height = 9cm

If a cross section is cut 3 cm from the base of the pyramid ,

1) Using unitary method ,

For the height of 9 cm the base is 72 cm squared

So, for the height of 1 cm the base is 72/9 cm squared.

Now, the cross section cut 3 cm base so height will become 6 cm.

Therefore , Area of cross section = 72/9 x 6

= 48 cm square

2) Volume of the pyramid = 1/2 x area x height

= 1/2 x 48 x 9

= 24 x 9

= 216 cm cube

Thus , the area of cross section is 48 cm square and volume is 216 cm cube.