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
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.
To find the volume of a pyramid, you can use the formula V = (1/3) * Bh, where V is the volume, B is the area of the base, and h is the height of the pyramid.
From the given image, the base of the pyramid is a square with sides measuring 20 feet. Therefore, the area of the base is 20 feet * 20 feet = 400 square feet.
The height of the pyramid is not provided in the image, so the volume cannot be determined. Without the height, we cannot calculate the volume of the pyramid.
Therefore, the correct answer is not given in the options.