Solved: Liam baked a very large cherry pie that he cuts into slices to share with his... [IB Mathematics Analysis and Approaches (AA)]

Solved: Liam baked a very large cherry pie that he cuts into slices to share with his... [IB Mathematics Analysis and Approaches (AA)] | RevisionDojo

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Question

SLPaper 1

Liam baked a very large cherry pie that he cuts into slices to share with his friends. The smallest slice is cut first. The volume of each successive slice of pie forms a geometric sequence.

The second smallest slice has a volume of $30 \, \text{cm}^3$ . The fifth smallest slice has a volume of $240 \, \text{cm}^3$ .

Find the volume of the smallest slice of pie.

[4]

Verified

Solution

State the equations for the given terms: $u_1 r = 30$ and $u_1 r^4 = 240$ OR $30r^3 = 240$ M1
Solve for the common ratio: $r = 2$ A1
Substitute $r$ to find the first term: $u_1(2) = 30$ OR $u_1(2)^4 = 240$ M1
Find the volume of the smallest slice: $u_1 = 15$ A1

4 marks total

NoteAward M1 for correct substitution in geometric sequence formula.

The cherry pie has a volume of $61\,425\,\text{cm}^3$ .

Find the total number of slices Liam can cut from this pie.

[2]

Verified

Solution

Substitute values into the geometric series sum formula equated to the total volume: $\frac{15(2^n - 1)}{2 - 1} = 61425$ M1
Find the number of slices: $n = 12$ A1

2 marks total

Mathematics Analysis and Approaches (AA) International Baccalaureate (IB) Practice Question: Liam baked a very large cherry pie that he cuts into slices to share with his friends. The smallest slice is cut first....