find the volume of a pyramid with a square base, where the side length of the base is 18.2 in and the height…

Explanation:

Step1: Recall the volume formula for a square - based pyramid

The volume (V) of a pyramid with a square base is given by the formula (V=\frac{1}{3}Bh), where (B) is the area of the base and (h) is the height of the pyramid. For a square base with side length (s), the area of the base (B = s^{2}). So the formula for the volume of a square - based pyramid can be written as (V=\frac{1}{3}s^{2}h).

Step2: Calculate the area of the base

Given that the side length of the square base (s = 18.2) in. Then the area of the base (B=s^{2}=(18.2)^{2}) square inches. ((18.2)^{2}=18.2\times18.2 = 331.24) square inches.

Step3: Substitute the values of (B) and (h) into the volume formula

We know that (h = 28.8) in and (B = 331.24) square inches. Substitute these values into the formula (V=\frac{1}{3}Bh). (V=\frac{1}{3}\times331.24\times28.8)

First, calculate (\frac{1}{3}\times331.24=\frac{331.24}{3}\approx110.4133)

Then, multiply this result by (28.8): (110.4133\times28.8 = 110.4133\times(20 + 8+0.8)=110.4133\times20+110.4133\times8 + 110.4133\times0.8) (110.4133\times20 = 2208.266) (110.4133\times8=883.3064) (110.4133\times0.8 = 88.33064)

Add these results together: (2208.266+883.3064 + 88.33064=2208.266+(883.3064 + 88.33064)=2208.266 + 971.63704=3179.90304)

Step4: Round the answer to the nearest tenth

The number (3179.90304) rounded to the nearest tenth is (3179.9) (since the hundredth digit is (0), which is less than (5), we don't round up the tenth digit).

Answer:

(3179.9)