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The radius of a right circular cylinder increased by 50%. Find the percentage increase in volume.

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120 %

125 %

150 %

130 %

answer is B.

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Detailed Solution

Suppose the radius of given cylinder is (r

) = 100 cm

Height

(h)

= 100 cm

.
Volume of cylinder,

(V) = π r^{2} h

\begin{matrix} V = π \times 100 \times 100 \times 100 \\ V = 1000000 π \end{matrix}

Now radius is increased by 50%. So, new radius

r_{n} = (100 + 50) cm

r_{n} = 150 cm

New volume,

\begin{matrix} V_{n} = π \times 150 \times 150 \times 100 \\ V_{n} = 2250000 π \end{matrix}

Now, Volume increase of cylinder

\begin{matrix} = 2250000 π - 1000000 π \\ = 1250000 π \end{matrix}

Now, percentage increase,

= \frac{1250000}{1000000} \times 100

= 125 %

Hence, this is the answer.
Option 2 is correct.

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