Find the values and arrange in increasing order:

(A) If each edge of a cube is increased by 20%, then the percentage increase in its volume is:

(B) If the radius of a cylinder is increased by 20%, while height increase 10%, then the percentage increase in the volume of the cylinder

(C) If each edge of a cube is increased by 20%, then the percentage increase in its surface area is:

(D) If the radius of a sphere is increased by 10%, then the percentage increase in its volume is:

Choose the correct order:

(A) Cube Volume - Edge increased by 20%

Original edge = $a$

Volume of cube = $a^3$

New edge = $a + 0.2a$

$= 1.2a$

Original volume = $a^3$

New volume = $(1.2a)^3$

$= 1.728a^3$

Increase = $1.728a^3 - a^3$

$= 0.728a^3$

Percentage increase = $\dfrac{0.728a^3}{a^3} \times 100$

$= 72.8\%$

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(B) Cylinder Volume - Radius increased by 20%, Height increased by 10%

Original radius = $r$, height = $h$

Volume of cylinder = $\pi r^2h$

New radius = $1.2r$

New height = $1.1h$

Original volume = $\pi r^2h$

New volume = $\pi(1.2r)^2(1.1h)$

$= \pi \times 1.44r^2 \times 1.1h$

$= 1.584\pi r^2h$

Increase = $1.584\pi r^2h - \pi r^2h$

$= 0.584\pi r^2h$

Percentage increase = $\dfrac{0.584\pi r^2h}{\pi r^2h} \times 100$

$= 58.4\%$

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(C) Cube Surface Area - Edge increased by 20%

Surface area of cube = $6a^2$

New edge = $1.2a$

Original surface area = $6a^2$

New surface area = $6(1.2a)^2$

$= 6 \times 1.44a^2$

$= 8.64a^2$

Increase = $8.64a^2 - 6a^2$

$= 2.64a^2$

Percentage increase = $\dfrac{2.64a^2}{6a^2} \times 100$

$= 44\%$

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(D) Sphere Volume - Radius increased by 10%

Volume of sphere = $\dfrac{4}{3}\pi r^3$

New radius = $1.1r$

Original volume = $\dfrac{4}{3}\pi r^3$

New volume = $\dfrac{4}{3}\pi(1.1r)^3$

$= \dfrac{4}{3}\pi \times 1.331r^3$

$= 1.331 \times \dfrac{4}{3}\pi r^3$

Percentage increase = $(1.331 - 1) \times 100$

$= 33.1\%$

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Summary of Results:

(A) Cube Volume: $72.8\%$

(B) Cylinder Volume: $58.4\%$

(C) Cube Surface Area: $44\%$

(D) Sphere Volume: $33.1\%$

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Arranging in increasing order:

$33.1\% < 44\% < 58.4\% < 72.8\%$

Therefore: (D), (C), (B), (A)