What is the volume of a square pyramid with base edges 54 yd and a slant height 45 yd?

Answer 1

To find the volume of a square pyramid, we use the formula ( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} ). The base area of the square is ( 54 , \text{yd} \times 54 , \text{yd} = 2916 , \text{yd}^2 ). To find the height, we can use the Pythagorean theorem: ( h = \sqrt{45^2 - (27)^2} = \sqrt{2025 - 729} = \sqrt{1296} = 36 , \text{yd} ). Therefore, the volume is ( V = \frac{1}{3} \times 2916 \times 36 = 34992 , \text{yd}^3 ).