Question

You are creating a wedding cake for a couple. The couple has already picked out a design that they like. The cake is composed of three tiers. Each tier is a square prism. The bottom tier has a length of 20 inches. The second tier has a length of 14 inches and the top tier has a length of 8 inches. Each tier has a height of 6 inches. The surface of the entire cake will need to be covered in frosting. How many cans of frosting will you need to buy, if each can covers 250 square inches?

Answer 1

Used Area from bottom box (green)= All 4 vertical faces +EFGH-IJKL
=(20*6+6*6+20*6+6*6)+20*6-14*6= 348 Square inches ...(i)

------------------------------------------------------------------------------------------------------

Used Area from middle box (Blue)= All 4 vertical faces +MNOP-QRST
=(14*6+6*6+14*6+6*6)+14*6-8*6=276 square inches...(ii)

------------------------------------------------------------------------------------------------------

Used Area from top box (Brown)= All 4 vertical faces +UVWX
=(8*6+6*6+8*6+6*6)+8*6=216 square inches...(iii)

------------------------------------------------------------------------------------------------------

so the surface area of the cake to be covered= 348+276+216=840 square inches.

given that 1 can covers 250 square inches

so number of cans needed = 840/250=3.36

which means 4 cans needed.