We can use the formula for the volume of a pyramid, which is V = (1/3)Bh, where B is the area of the base and h is the height.
From the diagram, we can see that the base is a square with side length 20 ft, so its area is B = 20^2 = 400 ft^2.
To find the height, we can use the fact that the slant height of the pyramid is 25 ft. This slant height is the hypotenuse of a right triangle with legs of 20 ft (half the length of the base) and h (the height of the pyramid). Using the Pythagorean theorem:
25^2 = 20^2 + h^2
625 = 400 + h^2
h^2 = 225
h = 15
Now we can plug in B = 400 and h = 15 into the formula for volume:
V = (1/3)(400)(15) = 2,000 ft^3
Rounding to the nearest tenth gives V ≈ 1,300.0 ft^3.
Therefore, the answer is (a) 1,300.0 ft^³.
What is the volume of the square pyramid shown to the nearest tenth?The figure is not drawn to scale.
Image: www(dot)connexus(dot)com/content/media/941080-7222013-25617-PM-1862038995(dot)gif
a. 1,300.0 ft³
b. 1,200.0 ft³
c. 433.3 ft³
d. 400.0 ft³
1 answer