Question

Match the correct statement with the given information.(4 points)
1) A cone's radius increases x 3 --->
The cone's volume will increase x 9

2) A cone's height increases x 3 --->
The cone's volume will increase x 3

3) A sphere's radius increases x 3 --->
The sphere's volume will increase x 27

4) A cylinder's radius increases x 6 --->
The cylinders volume will increase x 36

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Answer 1

All four statements are correct.

Brief reasons:
1) Cone: V = (1/3)πr^2h, so r ×3 → V ×3^2 = ×9.
2) Cone: V ∝ h, so h ×3 → V ×3.
3) Sphere: V = (4/3)πr^3, so r ×3 → V ×3^3 = ×27.
4) Cylinder: V = πr^2h, so r ×6 → V ×6^2 = ×36.