Question

use the cylinder shown to mark each statement as true or false. rewrite any false statements.

1. the height of the cylinder is 4 feet.

1. the area of the base is equal to \\( \pi ( 4 ^ { 2 } ) \\).

1. the volume of the cylinder is \\( 31.4 \mathrm { ft } ^ { 3 } \\).

Explanation:

9. Check the height statement

The height of the cylinder is given as \(h = 2.5\) ft (from the diagram), not \(4\) ft. So the statement "The height of the cylinder is \(4\) feet" is false.

10. Check the base - area statement

The formula for the area of the base of a cylinder (which is a circle) is \(A=\pi r^{2}\). Given \(d = 4\) ft, then \(r=\frac{d}{2}=2\) ft. The area of the base \(A=\pi(2^{2})\), not \(\pi(4^{2})\). So the statement "The area of the base is equal to \(\pi(4^{2})\)" is false.

11. Check the volume statement

The formula for the volume of a cylinder is \(V = A\times h=\pi r^{2}h\). Since \(r = 2\) ft and \(h=2.5\) ft, then \(V=\pi\times(2)^{2}\times2.5=\pi\times4\times2.5 = 10\pi\approx10\times3.14 = 31.4\) \(ft^{3}\). So the statement "The volume of the cylinder is \(31.4\) \(ft^{3}\)" is true.

Answer:

1. False
2. False
3. True