Question

The slant height of a square pyramid is 25cm and its surface area is 896 square centimetres. what is its volume​

Answer 1

Answer:

Let the side of the square base be x.

Surface area is made of a square with area x^2 and 4 triangles, each of them of height 25 and base x.

Total surface area then is:

x^2 + 4 x (25 x/2) = x^2 + 50 x = 896

Solving the equation:

x^2+50x−896=0 with the quadratic formula, you get x=14.

To calculate the volume, you need the vertical height of the pyramid — call it H — and H is part of a right-angled triangle in which the other leg is half of the side of the base — meaning, 7 cm — and the hypotenuse is the slant height 25cm.

Pythagoras’ theorem:

25^2 = H^2 + 7^2

Now, solve.....

The volume of a pyramid is area of the base times vertical height, divided by 3.

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