Question

Rodayna is making a huge cake in the shape of a house. The cake is a square prism with a pyramid on top. Rodayna’s made enough batter for 10,000 in3 of cake and enough frosting to frost 3000 in2 of cake. Does she have enough frosting and batter to make this cake? (She does not frost the bottom of the cake.) The formula for the volume of a right pyramid is , where 1/3 B is the area of the base and h is the distance from the center of the base of the pyramid to its vertex.

Answer 1

Volume of the cake= volume of right pyramid + volume of cube below the pyramid = 1/3 (b)(h) + b^3 where b = 19.5 and h = 13 plug these value into the formula, you get 7502.875, the volume is less than 10, 000. remember that the batter can supply 10, 000 in^3 of cake and the cake that you are making is only 7499 in ^ 3 so she has enough. now let's move on with the frosting. Surface area. we need the formula of a triangle and a square. formula of triangle is bh/2 and square area is b^2. let's do the pyramid first. how many triangles are there for the pyramid? 4 so we have to multiply the number of triangles to the area of one triangle to get the s.a. for each. Area = 4 x 1/2 bh base = 19.5 height= 13 plug your given values in the formula and you'll get? 507 now let's move on with the surface area of the cube. how many squares(sides) are there in a cube? 5 since she does not frost the cake at the bottom, we will only find the area of 5 squares. area of a square is b^2 So 5 x b^2 b=19.5 what will you get? 1901.25 now add the area of the triangles to the area of the squares, 2408.25 is it less than or greater than 3000 in^2 ? less the frosting that she has can cover 3000 in^2 of a cake. you have 2408.2 in^2 cake, so does that frosting enough or nah? remember 2408 is LESS than 3000, so it means she has more so the frosting is enough to cover your cake :) therefore, both the frosting and the batter are enough to make your house cake !