MATH SOLVE

2 months ago

Q:
# A solid right pyramid has a square base. The base edge length is 2 cm longer than the height of the pyramid.If the height is 6 cm, the volume of the pyramid is ____cm3.

Accepted Solution

A:

Answer:The volume of the pyramid is 128 cm³Step-by-step explanation:* Lets revise the volume of the pyramid- The pyramid has one base and the number of side faces depends on the number of sides of the base- The volume of any pyramid is 1/3 × Area of its base × its height* Lets solve the problem- The pyramid has a square base- It has four side faces all of them are triangles- It has five vertices and eight edges- The area of the base = s², where s is the length of the side of the square- The volume of the pyramid is 1/3 × s² × h, where h is the height of the pyramid- The base edge length of the base is 2 cm longer than the height of the pyramid- The height of the pyramid is 6 cm∵ The length of the edge of the base is 2 cm longer than the height of the pyramid∵ The height of the pyramid (h) = 6 cm∴ The edge length of the base = 6 + 2 = 8 cm- The area of the base = s²∵ s = 8 cm∴ The area of the base (s²) = 8² = 64 cm²- The volume of the pyramid = 1/3 × s² × h∴ Its volume = 1/3 × 64 × 6 = 128 cm³* The volume of the pyramid is 128 cm³