Question

A right pyramid having square of diagonal 40,72 m as its base and height of 8 m will have capacity of:
A. 4689.87 m2
B. 4456.82 m2
C. 4266.67 m
D. 4166.55 m​

Answer 1

Given :

The diagonal of square base pyramid = 40√2 meters

The height of the pyramid = h = 8 meters

To Find :

The volume of the right pyramid

Solution :

∵  The base of pyramid is square , for any square

So, diagonal ² = side ² + side ²

Or,  2  side ² =  diagonal ²

Or,  2  side ² = ( 40√2  )²

Or,  2  side ² = 3200

Or, side ² = $\dfrac{3200}{2}$

i.e side ² = 1600

∴  side = $\sqrt{1600}$

Or, side = 40 m

Each side of square base = side = 40 m,

Again

∵ The volume of the right pyramid = $\dfrac{1}{3}$ × side ² × height

Or,                                                     =  $\dfrac{1}{3}$ × (40 m) ² × 8 m

Or,                                                     =  $\dfrac{1}{3}$ × 1600 m² × 8 m

∴                                                        = 4266.67 m³

Hence, The capacity of square base right pyramid is 4266.67 cubic meters Answer