SOLUTION: 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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Question 1065774: 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? Found 2 solutions by addingup, ikleyn:Answer by addingup(3677) (Show Source):
You can put this solution on YOUR website! Volume: 1/3 x base area x height
1/3 x b x 4 = 48
b x 4 = 144
b = 36
The base is square, four identical sides. Thus, the area is s^2. Now we have:
s^2 = 36
s = 6 this is one side of the base and is the base of each of our four triangles, each of our sides.
The slant height:
½base^2+height^2 = slant height^2
½(6)^2+4^2 = slant height^2
9+16 = 25
sqrt25 = 5 this is the slant height
The surface area of the triangle:
1/2b × h = area
½(6) × 5 = area
area = 15
We have 4 sides: 15 × 4 = 60
Plus area of the base: s^2 = 6^2 = 36
Total 60+36 = 96 is the total area of the pyramid
You can put this solution on YOUR website! .
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.