Question

The square based pyramid is cut horizontally at a height of 15cm to leave this frustum. Calulate the volume of the frustum.

Answer 1

The answer is given below

Explanation:

The question is not complete. The correct question is:

A square based pyramid have a height of 30 cm and base of 10 cm. The The square based pyramid is cut horizontally at a height of 15cm to leave this frustum.

Answer:

The frustum would have a base of 10 cm and height of 15 cm. The lower base has a length of 10 cm. to calculate the upper base, we use the formula:

`(height\ of\ frustum)/(height\ of \ pyramid)=(base \of\ upper\ edge)/(base \of\ lower\ edge)`

Substituting:

`(30)/(15)=(10)/(b) \\ b=15*10/30=5`

The volume of the frustum is given by the formula:

`V=(h)/(3)(A_1+A_2+√(A_1A_2) )`

Where h is the height of the frustum = 15 cm, A1 is the area of the lower base = 10 * 10 = 100 cm², A1 is the area of the upper base = 5 * 5 = 25 cm²

Substituting gives:

`V=(h)/(3)(A_1+A_2+√(A_1A_2) )=(15)/(3)(100+25+√(100*25) )= 875\ cm^3`