A cake is cut into two equal parts and each part is again cut into two equal halves and it continues in that way. How many times should one cut the cake so that the number of pieces will be 32? [3 MARKS]

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Solution

Concept : 1 Mark
Application : 1 Mark
Calculation : 1 Mark

Number of pieces cut the first time = 2

$2 = 2^{1}$

Number of pieces cut the second time = 4

$4 = 2^{2}$

Number of pieces cut the third time = 8

$8 = 2^{3}$

Therefore the number of times the cake should be cut in order to obtain 32 pieces are:

$2^{n} = 32$

$2^{n} = 2^{5}$

$n = 5$

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