What is the volume of the pyramid to the nearest whole unit?
A pyramid with a rectangular base is shown. The base has sides of length 6 yards and 11 yards. From an 11 yard side, a dashed line is drawn to the center of the rectangle. From this point, a vertical dashed line extends upward to the vertex at a height of 6 yards above. A small square is located at the intersection of the dashed lines.
A. 99 yd3
B. 132 yd3
C. 198 yd3
D. 396 yd3
To find the volume of the pyramid, we need to use the formula:
Volume = (1/3) x base area x height
First, we need to find the area of the rectangular base:
Area = length x width
Area = 6 yards x 11 yards
Area = 66 square yards
Next, we need to find the height of the pyramid. We can use the Pythagorean theorem to do this:
a^2 + b^2 = c^2
where a and b are the sides of the base rectangle, and c is the height of the pyramid.
a = 6 yards
b = 11 yards
c = ?
6^2 + 11^2 = c^2
36 + 121 = c^2
157 = c^2
c = √157
c ≈ 12.53 yards
Now we can plug in the values into the formula:
Volume = (1/3) x base area x height
Volume = (1/3) x 66 square yards x 12.53 yards
Volume ≈ 131.98 cubic yards
Rounding to the nearest whole unit, the volume of the pyramid is approximately 132 cubic yards. Therefore, the answer is B. 132 yd3.