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The volume of a pyramid is 48 cubic feet. What is its total surface area if the pyramids height is 4 feet and the base is a square?
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the base is a square, four identical sides. The area is s^2
Volume of the pyramid:
= 48 --->
4s^2 = 3*48
s^2 = (3*48)/4
s^2 = 36 ---> s = sqrt(36) ----> s = 6 feet
Each side of the pyramid is a triangle.
Lateral height of the pyramid is the height of the lateral side.
+ = --->
= = ----> = 5 inches.
Area of each lateral side is = (6*5)/2 = 15 square feet. This is one side.
Our pyramid has four sides:
4*15 = 60 square feet. It is the surface area of four lateral sides.
The base area = s^2 = 6^2 = 36
Total area, four sides plus base:
36 + 60 = 96 square feet. It is the total area of the pyramid.
SOLVED.
Lessons on surface area of pyramids in this site:
- Surface area of pyramids
- Solved problems on surface area of pyramids
Also, you have this free of charge online textbook on Geometry
GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.
The referred lessons are the part if this textbook under the topic "Surface area of 3D solid bodies".
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You demonstrated very low level of knowledge on the subject working on this solution.
I am very disappointed.