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. ?

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I don't understand how I am supposed to use that information to relay it onto the square pyramid?

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Answer 1 · 2018-04-22T18:35:59

#color(blue)(6.75)# nearest hundreth.

The surface area of a cone is given by:

#"Area"=pirl+pir^2#

The surface area of a square based pyramid is:

#4(1/2xxbxxs)+b^2#

Where #b="base length"# and #s="slant height"#

First calculate the surface area of the cone:

#"Area=pi(4)(5)+pi(4)^2=36pi#

Surface area of pyramid is equal to this:

#4(1/2xxbxxs)+b^2=36pi#

We know slant height is #5#, so:

#4(1/2xxbxx(5))+b^2=36pi#

#10b+b^2=36pi#

#10b+b^2-36pi=0#

Using the quadratic formula:

#b=(-(10)+-sqrt((10)^2-4(1)(36pi)))/2#

#b=(-10+-sqrt((100+144pi)))/2#

#b=(-10+-2sqrt((25+36pi)))/2#

#b=-5+-sqrt((25+36pi))#

#b=-5+sqrt((25+36pi))=6.75# 2 d.p.

Negative value no valid for length.