Mathematics: The figure is a square based pyramid. Total surface area of the pyramid is 9072m³. If the length of the side of the square base is 56 cm , find the volume of the pyramid. Help!! :)

If you convert everything to inches you will get: 66 x33 . So multiplying those you get 2176sq inches....

The figure is a square based pyramid. Total surface

322993

30.12.2021

The volume of the pyramid=47040 m^3

Solution Given:

The total surface area of the pyramid = $9072\:m^2$

let the height be AB be h.

length of side[l]=56 m

The volume of the pyramid=?

let slant height be AC=a.

and BC=b

we have,

The perimeter of base[P]=4l=4*56=224m

BC=28m

Now;

The total surface area of the pyramid = $9072\:m^2$

lateral= surface area +base area= $9072\:m^2$

$\frac{1}{2}*P*a+l^2=9072\:m^2$

$\frac{1}{2}*224*a+56^2=9072\:m^2$

112a=9072-3136

$a=\frac{5936}{112}=53m$

now

By using Pythagoras law;

AC^2=AB^2+BC^2

a^2=h^2+b^2

53^2=h^2+28^2

h^2=2809-784

$h=\sqrt{2025}$

h=45m

now,

The volume of the pyramid= $\frac{1}{3}*l^2*h$

$\frac{1}{3}*56^2*45=47040m^3$

Step-by-step explanation:

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