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) About Me  (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

Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
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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:

%281%2F3%29%2As%5E2%2A4 = 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.

H%5E2 + %28s%2F2%29%5E2 = H%5Blateral%5D%5E2  --->

H%5Blateral%5D%5E2 = 4%5E2+%2B+3%5E2 = 25  ---->  H%5Blateral%5D = 5 inches.


Area of each lateral side is b%2AH%5Blateral%5D%2F2 = (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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Dear tutor "addingup".

You demonstrated very low level of knowledge on the subject working on this solution.

I am very disappointed.