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?

Question

(1 point)
Responses

27
27

213
213

214
214

640

Answer 1

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.