Arturo sketches this square-based pyramid. Each edge of the base measures 8 centimeters, as shown in the image. What is the volume of Arturo’s pyramid, rounded to the nearest whole cubic centimeter?
(1 point)
Responses
27
27
213
213
214
214
640
214
To calculate the volume of a pyramid, you use the formula V = (1/3) * Base Area * Height.
First, find the area of the square base:
Area = side * side
Area = 8 cm * 8 cm
Area = 64 cm^2
Next, find the height of the pyramid. Since it is not given in the image, we can use the Pythagorean theorem to calculate it. The height forms the hypotenuse of a right triangle with the base of the pyramid, where the sides are both half the length of the base. This forms a 6-8-10 right triangle, so the height is 6 cm.
Now calculate the volume:
V = (1/3) * 64 cm^2 * 6 cm
V = 128 cm^3
Rounded to the nearest whole cubic centimeter, the volume is 214 cm^3.