Question

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 volume of sphere P as a fraction of sphere R. Write your answer in the form a/b

Answer 1

Answer:

1/2.25

Step-by-step explanation:

let volume of P be x

Q will be 1.5x

R will be 150/100* 1.5x which is 2.25x

P/R = x/ 2.25x

= 1/2.25

Answer 2

Here we need to write the volume of sphere P as a fraction of the volume of sphere R.

We will get:

$V_P = V_R/2.25$

The given information is:

• 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.

From the first statement, we can write:

$V_Q = (1.5)*V_P$

Where the 1.5 comes because the volume of sphere Q is 150% of the volume of sphere P.

From the second statement we can write:

$V_R = (1.5)*V_Q$

We can rewrite this last one as:

$V_Q = V_R/(1.5)$

Now we can replace this on the first equation to get:

$V_R/(1.5) = (1.5)*V_P\\\\V_P =V_R/(1.5)^2 = V_R/2.25$

This is the equation we wanted, the volume of sphere P as a fraction of the volume of the sphere R.

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