1 answer

Two pyramids are similar. Pyramid A has a volume of 32m^3 and with a surface area of 100m^2 while Pyramid

Question:

Two pyramids are similar. Pyramid A has a volume of 32m^3 and with a surface area of 100m^2 while Pyramid B has a volume of 500m^3 and is 60m tall. What is the height of Pyramid A? What is the surface area of Pyramid B?

Answers

#"3.84 m, 1562.5 m"^2#

Explanation:

Pyramids #"A"# and #"B"# are similar. So,

#"Volume of pyramid A"/"Height of pyramid A" = "Volume of pyramid B"/"Height of pyramid B"#

#(32\ "m"^3)/("H"_"A") = ("500 m"^3)/("60 m")#

#"H"_"A" = "60 m" × (32 cancel("m"^3))/(500 cancel("m"^3)) = color(blue)("3.84 m")#

Similarly,

#"Volume of pyramid A"/"Surface Area of pyramid A" = "Volume of pyramid B"/"Surface Area of pyramid B"#

#("32 m"^3)/("100 m"^2) = ("500 m"^3)/("A"_"B")#

#"A"_"B" = "100 m"^2 × (500 cancel("m"^3))/(32 cancel("m"^3)) = color(blue)("1562.5 m"^2)#

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