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Here are three spheres - Edexcel - GCSE Maths - Question 12 - 2019 - Paper 1

Question 12

Here are three spheres. The volume of sphere Q is 50% more than the volume of sphere P. The volume of sphere R is 50% more than the volume of sphere Q. Find the vo... show full transcript

Worked Solution & Example Answer:Here are three spheres - Edexcel - GCSE Maths - Question 12 - 2019 - Paper 1

Step 1

The volume of sphere Q is 50% more than the volume of sphere P.

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Answer

Let the volume of sphere P be denoted as ( V_P ). Then, the volume of sphere Q can be expressed as:

$V_Q = V_P + 0.5 \times V_P = 1.5 V_P$

Step 2

The volume of sphere R is 50% more than the volume of sphere Q.

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Answer

Now, substituting for the volume of sphere Q:

$V_R = V_Q + 0.5 \times V_Q = 1.5 V_Q = 1.5 \times 1.5 V_P = 2.25 V_P$

Step 3

Find the volume of sphere P as a fraction of the volume of sphere R.

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Answer

To find the volume of sphere P as a fraction of sphere R:

$\frac{V_P}{V_R} = \frac{V_P}{2.25 V_P} = \frac{1}{2.25} = \frac{4}{9}$

Thus, the volume of sphere P as a fraction of the volume of sphere R is ( \frac{4}{9} ).

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