Answer:
Explanation:
A square pyramid's height-to-slant height ratio is expressed as 4:5
Given that the TSA of a square pyramid is 96 cm, let the height be 4x and the slant height be 5x.
TSA = LSA + area of the base (eq1)
LSA = base perimeter x slant height / 2
Here, the ratio is radius = side of base / 2
we have a relation,
l^2 = r^2 + h^2
(5x)^2 = (s/2)^2 + (4x)^2
√[25x^2 - 16x^2 ] = s/2
√9x^2 = s/2
=> s = 6x cm
from eq(1) ,
96 = 4s × 5x /2 + s^2
=> 96 = 60x^2 + 36x^2
=> 96 = 96x^2
=> x = 1cm
Therefore, height is 4(1) = 4cm,
slant height is 5(1) = 5cm,
side is 6cm.
Area of base x Height = Volume of Pyramid
= s^2 × 4/3 = 36 × 4 /3 = 48cm^3