Consider the volumes of the following:

(A) A cylinder with a radius of base 7 cm and height 10 cm.

(B) A cone of radius 7 cm and height 9 cm.

(C) A sphere of radius 6 cm.

The volumes of these figures in decreasing order shall be:

Choose the correct answer from the options given below:

The volume formulas needed are:

Cylinder: $V = \pi r^2 h$

Cone: $V = \frac{1}{3}\pi r^2 h$

Sphere: $V = \frac{4}{3}\pi r^3$

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For the cylinder with radius $r = 7$ cm and height $h = 10$ cm:

$V_A = \pi r^2 h$

$V_A = \pi \times (7)^2 \times 10$

$V_A = \pi \times 49 \times 10$

$V_A = 490\pi$ cm³

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For the cone with radius $r = 7$ cm and height $h = 9$ cm:

$V_B = \frac{1}{3}\pi r^2 h$

$V_B = \frac{1}{3} \times \pi \times (7)^2 \times 9$

$V_B = \frac{1}{3} \times \pi \times 49 \times 9$

$V_B = \frac{1}{3} \times \pi \times 441$

$V_B = 147\pi$ cm³

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For the sphere with radius $r = 6$ cm:

$V_C = \frac{4}{3}\pi r^3$

$V_C = \frac{4}{3} \times \pi \times (6)^3$

$V_C = \frac{4}{3} \times \pi \times 216$

$V_C = \frac{864}{3} \times \pi$

$V_C = 288\pi$ cm³

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Comparing the volumes:

Cylinder (A): $490\pi$ cm³

Sphere (C): $288\pi$ cm³

Cone (B): $147\pi$ cm³

The decreasing order is: (A), (C), (B)