SOLUTION: A regular square pyramid is inscribed in a come with radius 4 cm. and height 4 cm. A. What is the volume of the pyramid? I know that the volume of the pyramid equals Lateral

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Question 83754This question is from textbook Geometry
: A regular square pyramid is inscribed in a come with radius 4 cm. and height 4 cm.
A. What is the volume of the pyramid?
I know that the volume of the pyramid equals Lateral Area+Base, which is P being the perimeter of the base and L being the slant height. I am not able to get beyond this point on matter how hard I try.
B. Find the slant height of the pyramid and the cone.
I have tried at this one many times but have not been able to get anything. I know that the slant height forms a triangle with the radius and the height, but I do not know where to go from there.
Please help me! This question is from textbook Geometry

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A regular square pyramid is inscribed in a come with radius 4 cm. and height 4 cm.
Draw the figure of the reg sq pyramid in the cone; draw the diameter = 8 cm
of the base of the cone; draw the altitude = 4 cm of the pyramid = the altitude
of the cone.
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A. What is the volume of the pyramid?
V = (1/3)(area of base)(altitude)
The diagonal of the base is the diameter of the cone = 8 cm
Radius of the base = 4 cm
Side of the square base = 4/sqrt2
Therefore Area of the base = (side)^2 = (4/sqrt2)^2 = 16/2 = 8 sq cm
So, Volume = (1/3)(8)(4) = 32/3 cu cm.
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I know that the volume of the pyramid equals Lateral Area+Base, which is P being the perimeter of the base and L being the slant height. I am not able to get beyond this point on matter how hard I try.
B. Find the slant height of the pyramid and the cone.
Draw the slant height of the pyramid.
It is the hypotenuse of a rt. triangle with sides 4 and (1/2)(4/sqrt2)
or 4 and 2sqrt2.
hyp^2=(2sqrt2)^2+4^2 = = 8 + 16 = 24
hyp = 2sqrt6
So, slant height of the pyramid = 2sqrt6 cm
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Cheers,
Stan H.