Question

a sculptor started with a solid cube and then carved out a pyramid from the top of it. the pyramid has the same base and same height as the cube. image of a cube with side length 6 m the volume of the solid figure that remained is ______ cubic meters. the solution is blank.

Explanation:

Step1: Calculate the volume of the cube

The formula for the volume of a cube is \( V_{cube} = s^3 \), where \( s \) is the side length. Here, \( s = 6 \) m.
So, \( V_{cube} = 6^3 = 216 \) cubic meters.

Step2: Calculate the volume of the pyramid

The formula for the volume of a pyramid is \( V_{pyramid} = \frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height. Since the base and height of the pyramid are the same as the cube, the base area \( B = s^2 = 6^2 = 36 \) square meters and \( h = 6 \) m.
So, \( V_{pyramid} = \frac{1}{3} \times 36 \times 6 = 72 \) cubic meters.

Step3: Calculate the remaining volume

Subtract the volume of the pyramid from the volume of the cube: \( V_{remaining} = V_{cube} - V_{pyramid} = 216 - 72 = 144 \) cubic meters.

Answer:

144