Question

A right cone with a radius of 4 inches and a square pyramid both have a slant height of 5 inches. Both solids have the same surface area. Find the length of a base edge of the pyramid. Round your answer to the nearest hundredth.

Answer 1

The surface area of the cone is given by:
SA=πrl
Thus the surface area of the cone will be:
SA=π×4×5
SA=20π=63.932

Surface area of the pyramid is given by:
SA=1/2×4×(b×l)
thus the base length will be:
63.932=10l
thus
l=6.3932 in