Question

A cyclinder has a volume of 703Pi cm3 and a height of 18.5 cm. What can be concluded about the cyclinder? Check all that apply.
The formula for the volume of a cyclinder can be applied to find the area of the base.
To find the area of the base, multiply volume and height.
The radius of the cyclinder is half the height.
The area of the base is 38Pi cm2.
To verify the solution is correct, substitute the given measures and the solution into the equation and verify the result is a true statement.

Answer 1

To analyze the cylinder with a volume of \(703\pi \, \text{cm}^3\) and a height of \(18.5 \, \text{cm}\), let's go through each statement one by one.

1. **The formula for the volume of a cylinder can be applied to find the area of the base.**
- **True.** The volume \(V\) of a cylinder is given by the formula:
\[
V = A_b \times h
\]
where \(A_b\) is the area of the base and \(h\) is the height. Rearranging this formula allows us to find the area of the base.

2. **To find the area of the base, multiply volume and height.**
- **False.** To find the area of the base, you actually divide the volume by the height:
\[
A_b = \frac{V}{h}
\]
This statement incorrectly states the operation as multiplication instead of division.

3. **The radius of the cylinder is half the height.**
- **False.** The relationship between the radius and height does not imply that the radius is half the height. The radius can be found if we know the area of the base or the volume, but we can't assume a direct relationship between the height and radius without specific values.

4. **The area of the base is \(38\pi \, \text{cm}^2\).**
- **True.** We can find the area of the base using the volume formula:
\[
A_b = \frac{V}{h} = \frac{703\pi}{18.5}
\]
Calculating this gives:
\[
A_b = \frac{703\pi}{18.5} \approx 38\pi \, \text{cm}^2
\]

5. **To verify the solution is correct, substitute the given measures and the solution into the equation and verify the result is a true statement.**
- **True.** We can perform the substitution:
\[
V = A_b \times h
\]
Substituting the values:
\[
703\pi = 38\pi \times 18.5
\]
Simplifying the right side:
\[
38\pi \times 18.5 = 703\pi
\]
The equation holds true, confirming the calculations are correct.

In summary, the following conclusions can be made about the cylinder:
- The formula for the volume of a cylinder can be applied to find the area of the base.
- The area of the base is \(38\pi \, \text{cm}^2\).
- To verify the solution is correct, you can substitute the measures into the volume formula to check for accuracy.

The correct conclusions are statements 1, 4, and 5.