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Mathematics

Grade9

Easy

Question

The ratio of the height of solid P to the height of solid Q is 5 : 4. The volume of solid P is 150cm³. Calculate the volume of solid Q.

76.8
$\frac{384}{5}$

hint Hint:

We are given the ratio of height of solid P to solid Q. It is 5:3. We are given the value of the volume of solid P. We have to find the volume of solid Q.

The correct answer is: 76.8

The ratio of heights is 5:3
The volume of solid P is 150cm³.
Let us denote the volume of Q by "v".
We the ratio of the sides of the solids is given by a:b, then the ratio of the volume of the solid is give by a³:b³
$fraction numerator V o l u m e space o f space P over denominator V o l u m e space o f space Q end fraction equals a cubed over b cubed$
$fraction numerator 150 over denominator v end fraction equals fraction numerator a to the power of 3 end exponent over denominator b to the power of 3 end exponent end fraction$
$fraction numerator 150 over denominator v end fraction equals fraction numerator 5 to the power of 3 end exponent over denominator 4 to the power of 3 end exponent end fraction$
$fraction numerator 150 over denominator v end fraction equals fraction numerator 125 over denominator 64 end fraction$
v = 76.8 cm³
So, the volume of solid Q is 76.8 cm³.

For such questions, we should know Volume of different shapes.

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