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

Answer:

The answer is given below

Step-by-step 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:

$\frac{height\ of\ frustum}{height\ of \ pyramid}=\frac{base \of\ upper\ edge}{base \of\ lower\ edge}$

Substituting:

$\frac{30}{15}=\frac{10}{b} \\ b=15*10/30=5$

The volume of the frustum is given by the formula:

$V=\frac{h}{3}(A_1+A_2+\sqrt{A_1A_2} )$

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:

$V=\frac{h}{3}(A_1+A_2+\sqrt{A_1A_2} )=\frac{15}{3}(100+25+\sqrt{100*25} )= 875\ cm^3$