Cylinder Transformation

Geometry Level 2

If the height of a right cylinder is increased by 50% and the radius is decreased by 50%, the change in the volume of the cylinder is _____ \text{\_\_\_\_\_} %.

Note:
If the volume increases, give a positive number.
If the volume decreases, give a negative number.


The answer is -62.5.

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Pranshu Gaba by Pranshu Gaba , 22, India

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1 solution

Pranshu Gaba
Feb 12, 2016

The volume of the original cylinder is V = π r 2 h V = \pi r^{2} h . The volume of the new cylinder is

V ′ = π × ( 50 100 r ) 2 × 150 100 h = 375 1000 × π r 2 h = 375 1000 × V \begin{aligned} V' & = \pi \times \left(\dfrac{50}{100} r\right)^{2} \times \dfrac{150}{100} h \\ & = \frac{375}{1000} \times \pi r^{2} h \\ & = \frac{375}{1000} \times V \end{aligned}

The percentage change in volume is

V ′ − V V × 100 = 1000 − 375 1000 × 100 = − 62.5 □ \frac{V' - V}{V} \times 100 = \frac{ 1000 - 375 }{1000} \times 100 = \boxed{-62.5} ~~~~~_\square

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Yeah.The same way

Abhiram Rao - 5 years, 1 month ago

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