Smiths bakery is baking several large cakes for a community festival. The cakes consist of two geometrically similar shapes as shown. If 50 pieces of cake can be cut from the smaller cake, how many pieces of the same size can be cut from the larger cake? Round to the nearest piece of cake

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Find attached to this solved answer the diagram for this question

312.5 pieces of cake

Step-by-step explanation:

From the diagram, we where given the following parameters for :

a. The Large Cake

Length = 5ft

Breadth = 4ft

b. The Small cake

Length = 2ft

Breadth = 1.6ft

The shape of the cake is a square shape

Hence,

For the Large cake we would find the Area.

Area of a Square = Length × Breadth

Area of the Large cake = 5ft × 4ft

= 20ft²

Area of the Small cake = 2ft × 1.6ft

= 3.2ft²

For the question, 50 pieces of cake where taken from the smaller cake

We are to find how many pieces of cake can be taken from the smaller cake.

Hence if

3.2ft² of the small cake gives =50 pieces of cake

20ft² of the large cake gives = ?

We cross multiply

= (20ft² × 50 pieces) ÷ 3.2ft²

= 312.5 pieces of cake.

Hence the large cake would give us 312.5 pieces of cake.