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Here are three spheres - Edexcel - GCSE Maths - Question 14 - 2019 - Paper 1

Question 14

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 14 - 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:

$V_Q = V_P + 0.5 imes V_P = 1.5V_P.$

Step 2

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

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Answer

Now, the volume of sphere R can be denoted as:

$V_R = V_Q + 0.5 imes V_Q = 1.5V_Q.$

Substituting the expression for $V_Q$ , we get:

$V_R = 1.5(1.5V_P) = 2.25V_P.$

Step 3

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

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Answer

Now, to find the volume of sphere P as a fraction of the volume of sphere R:

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

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

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